12148:
182:
5040:
12134:
4638:
3094:
39:
12172:
12160:
5035:{\displaystyle \operatorname {R} _{\mathbf {X} \mathbf {Y} }={\begin{bmatrix}\operatorname {E} &\operatorname {E} &\cdots &\operatorname {E} \\\\\operatorname {E} &\operatorname {E} &\cdots &\operatorname {E} \\\\\vdots &\vdots &\ddots &\vdots \\\\\operatorname {E} &\operatorname {E} &\cdots &\operatorname {E} \end{bmatrix}}}
7666:
7959:
2948:
can be circular translation transform, rotation transform, or scale transform, etc. The kernel cross-correlation extends cross-correlation from linear space to kernel space. Cross-correlation is equivariant to translation; kernel cross-correlation is equivariant to any affine transforms, including
9349:
Caution must be applied when using cross correlation for nonlinear systems. In certain circumstances, which depend on the properties of the input, cross correlation between the input and output of a system with nonlinear dynamics can be completely blind to certain nonlinear effects. This problem
8193:
between the two signals, the maximum (or minimum if the signals are negatively correlated) of the cross-correlation function indicates the point in time where the signals are best aligned; i.e., the time delay between the two signals is determined by the argument of the maximum, or
7324:
7297:
can be estimated by averaging the product of samples measured from one process and samples measured from the other (and its time shifts). The samples included in the average can be an arbitrary subset of all the samples in the signal (e.g., samples within a finite time window or a
3089:
is maximized. This is because when peaks (positive areas) are aligned, they make a large contribution to the integral. Similarly, when troughs (negative areas) align, they also make a positive contribution to the integral because the product of two negative numbers is positive.
3948:
8556:
8312:
9350:
arises because some quadratic moments can equal zero and this can incorrectly suggest that there is little "correlation" (in the sense of statistical dependence) between two signals, when in fact the two signals are strongly related by nonlinear dynamics.
3843:
4121:
3097:
Animation of how cross-correlation is calculated. The left graph shows a green function G that is phase-shifted relative to function F by a time displacement of đ. The middle graph shows the function F and the phase-shifted G represented together as a
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applications in which the brightness of the image and template can vary due to lighting and exposure conditions, the images can be first normalized. This is typically done at every step by subtracting the mean and dividing by the
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1978:
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6676:
8962:
2608:
8407:
2903:
2397:
2263:
7059:
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across time are temporal cross-correlations. In probability and statistics, the definition of correlation always includes a standardising factor in such a way that correlations have values between â1 and +1.
4335:
3856:
5279:
5187:
8205:
7661:{\displaystyle \rho _{XX}(t_{1},t_{2})={\frac {\operatorname {K} _{XX}(t_{1},t_{2})}{\sigma _{X}(t_{1})\sigma _{X}(t_{2})}}={\frac {\operatorname {E} \left}{\sigma _{X}(t_{1})\sigma _{X}(t_{2})}}}
5245:
5514:
5454:
4481:
4421:
1020:
909:
7981:
8994:
8189:
are useful for determining the time delay between two signals, e.g., for determining time delays for the propagation of acoustic signals across a microphone array. After calculating the
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1164:
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9237:
6310:
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4004:
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7281:
6560:
5731:
3659:
2946:
7318:. However, in other disciplines (e.g. engineering) the normalization is usually dropped and the terms "cross-correlation" and "cross-covariance" are used interchangeably.
5661:
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4541:
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550:
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498:
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1983:
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1520:
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255:
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1371:
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8614:
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8364:
2764:
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6094:
6067:
5814:
5337:
2769:
1434:
1285:
1217:
830:
3340:
3246:
3217:
1197:
798:
2472:
856:
769:
714:
229:
9646:
Kapinchev, Konstantin; Bradu, Adrian; Barnes, Frederick; Podoleanu, Adrian (2015). "GPU implementation of cross-correlation for image generation in real time".
9213:
9193:
9173:
9153:
9133:
9113:
9093:
8747:
8696:
8579:
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6040:
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1305:
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904:
884:
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638:
618:
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1592:
2268:
2134:
7954:{\displaystyle \rho _{XY}(\tau )={\frac {\operatorname {K} _{XY}(\tau )}{\sigma _{X}\sigma _{Y}}}={\frac {\operatorname {E} \left}{\sigma _{X}\sigma _{Y}}}}
6924:
6681:
168:
7961:
The normalization is important both because the interpretation of the autocorrelation as a correlation provides a scale-free measure of the strength of
9804:
Tahmasebi, Pejman; Hezarkhani, Ardeshir; Sahimi, Muhammad (2012). "Multiple-point geostatistical modeling based on the cross-correlation functions".
9444:
Bracewell, R. "Pentagram
Notation for Cross Correlation." The Fourier Transform and Its Applications. New York: McGraw-Hill, pp. 46 and 243, 1965.
316:, which is the cross-correlation of a signal with itself, there will always be a peak at a lag of zero, and its size will be the signal energy.
11269:
9223:
2842:
11774:
11924:
9716:
Kun Il Park, Fundamentals of
Probability and Stochastic Processes with Applications to Communications, Springer, 2018, 978-3-319-68074-3
201:
is 1.0, the value of the result at 5 different points is indicated by the shaded area below each point. Also, the vertical symmetry of
11548:
10189:
3943:{\displaystyle {\mathcal {F}}\left\{f\star g\right\}={\overline {{\mathcal {F}}\left\{f\right\}}}\cdot {\mathcal {F}}\left\{g\right\},}
4270:
8551:{\displaystyle {\frac {1}{n}}\sum _{x,y}{\frac {1}{\sigma _{f}\sigma _{t}}}\left(f(x,y)-\mu _{f}\right)\left(t(x,y)-\mu _{t}\right)}
11322:
6571:
5250:
161:
11761:
5121:
3057:
function along the x-axis, calculating the integral of their product at each position. When the functions match, the value of
9785:
9743:
9701:
9663:
8832:
8763:
6508:
Note that this expression is not well-defined for all time series or processes, because the mean or variance may not exist.
105:
10184:
9884:
7978:
For jointly wide-sense stationary stochastic processes, the cross-correlation function has the following symmetry property:
7237:
is precisely the additional information (beyond being individually wide-sense stationary) conveyed by the requirement that
5192:
125:
3102:. Integrating F multiplied by the phase-shifted G produces the right graph, the cross-correlation across all values of đ.
90:
12203:
10788:
9936:
154:
5459:
5399:
4426:
4366:
9222:, a process used for finding instances of a pattern or object within an image. It is also the 2-dimensional version of
100:
3173:
ensures that aligned peaks (or aligned troughs) with imaginary components will contribute positively to the integral.
11571:
11463:
12176:
11749:
11623:
8967:
9730:. Proceedings of 2009 ASME International Mechanical Engineering Congress, Lake Buena Vista, FL. pp. 281â288.
9453:
Papoulis, A. The
Fourier Integral and Its Applications. New York: McGraw-Hill, pp. 244â245 and 252-253, 1962.
8307:{\displaystyle \tau _{\mathrm {delay} }={\underset {t\in \mathbb {R} }{\operatorname {arg\,max} }}((f\star g)(t))}
11807:
11468:
11213:
10584:
10174:
7315:
3838:{\displaystyle \left(f\star g\right)\star \left(f\star g\right)=\left(f\star f\right)\star \left(g\star g\right)}
4127:
algorithms, this property is often exploited for the efficient numerical computation of cross-correlations (see
4116:{\displaystyle {\mathcal {F}}\left\{{\overline {f(-t)}}\right\}={\overline {{\mathcal {F}}\left\{f(t)\right\}}}}
11858:
11070:
10877:
10766:
10724:
9630:
9525:
9492:
7965:, and because the normalization has an effect on the statistical properties of the estimated autocorrelations.
10798:
9115:
are real matrices, their normalized cross-correlation equals the cosine of the angle between the unit vectors
12213:
12101:
11060:
9963:
9370:
2093:
7302:
of one of the signals). For a large number of samples, the average converges to the true cross-correlation.
5520:, each containing random variables whose expected value and variance exist, the cross-correlation matrix of
11652:
11601:
11586:
11576:
11445:
11317:
11284:
11110:
11065:
10895:
5687:
is the correlation between values of the processes at different times, as a function of the two times. Let
2437:
2402:
648:
336:
12164:
11996:
11797:
11721:
11022:
10776:
10445:
9909:
9425:
4139:
3275:
7184:
6224:
5964:
5923:
5342:
5089:
2997:
differing only by an unknown shift along the x-axis. One can use the cross-correlation to find how much
1131:
1121:{\displaystyle (f\star g)(\tau )\ \triangleq \int _{-\infty }^{\infty }{\overline {f(t-\tau )}}g(t)\,dt}
1010:{\displaystyle (f\star g)(\tau )\ \triangleq \int _{-\infty }^{\infty }{\overline {f(t)}}g(t+\tau )\,dt}
12208:
11881:
11853:
11848:
11596:
11355:
11261:
11241:
11149:
10860:
10678:
10161:
10033:
9234:
NCC is similar to ZNCC with the only difference of not subtracting the local mean value of intensities:
8090:{\displaystyle \operatorname {R} _{XY}(t_{1},t_{2})={\overline {\operatorname {R} _{YX}(t_{2},t_{1})}}}
4128:
3706:
332:
284:. It is commonly used for searching a long signal for a shorter, known feature. It has applications in
30:
273:
of two series as a function of the displacement of one relative to the other. This is also known as a
11613:
11381:
11102:
11027:
10956:
10885:
10805:
10793:
10663:
10651:
10644:
10352:
10073:
9405:
5817:
3982:
1863:{\displaystyle (f\star g)(\tau )\ \triangleq \int _{t_{0}}^{t_{0}+T}{\overline {f(t-\tau )}}g(t)\,dt}
1735:{\displaystyle (f\star g)(\tau )\ \triangleq \int _{t_{0}}^{t_{0}+T}{\overline {f(t)}}g(t+\tau )\,dt}
641:
3954:
12096:
11863:
11726:
11411:
11376:
11340:
11125:
10567:
10476:
10435:
10347:
10038:
9877:
9778:
Nonlinear System
Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains
9390:
8323:
7240:
6519:
5690:
4350:
3623:
2915:
289:
60:
5638:
5545:
5523:
5067:
5045:
4524:
4502:
577:
555:
533:
507:
481:
459:
437:
411:
389:
363:
341:
12005:
11618:
11558:
11495:
11133:
11117:
10855:
10717:
10707:
10557:
10471:
9726:
Rhudy, Matthew; Brian Bucci; Jeffrey
Vipperman; Jeffrey Allanach; Bruce Abraham (November 2009).
8701:
7091:
5887:
5851:
4602:{\displaystyle \operatorname {R} _{\mathbf {X} \mathbf {Y} }\triangleq \ \operatorname {E} \left}
3107:
135:
70:
9484:
9477:
9003:
7671:
3060:
12198:
12043:
11973:
11766:
11703:
11458:
11345:
10342:
10239:
10146:
10025:
9924:
9857:
7962:
5284:
4612:
4124:
3469:
55:
9517:
9510:
8654:
7064:
3347:
2832:{\displaystyle k(\cdot ,\cdot )\colon \mathbb {C} ^{M}\times \mathbb {C} ^{M}\to \mathbb {R} }
1502:
719:
234:
12068:
12010:
11953:
11779:
11672:
11581:
11307:
11191:
11050:
11042:
10932:
10924:
10739:
10635:
10613:
10572:
10537:
10504:
10450:
10425:
10380:
10319:
10279:
10081:
9904:
7299:
7291:
7151:
7118:
5517:
1525:
1350:
8619:
8584:
8369:
8334:
8172:{\displaystyle \operatorname {R} _{XY}(\tau )={\overline {\operatorname {R} _{YX}(-\tau )}}}
5628:{\displaystyle \operatorname {R} _{\mathbf {Z} \mathbf {W} }\triangleq \ \operatorname {E} }
2613:
11991:
11566:
11515:
11491:
11453:
11371:
11350:
11302:
11181:
11159:
11128:
11037:
10914:
10865:
10783:
10756:
10712:
10668:
10430:
10206:
10086:
9813:
9385:
7311:
7294:
6283:
6256:
6072:
6045:
5792:
5676:
5310:
1419:
1270:
1202:
803:
9852:
3316:
3222:
3193:
1173:
774:
8:
12138:
12063:
11986:
11667:
11431:
11424:
11386:
11294:
11274:
11246:
10979:
10845:
10840:
10830:
10822:
10640:
10601:
10491:
10481:
10390:
10169:
10125:
10043:
9968:
9870:
9648:
2015 9th
International Conference on Signal Processing and Communication Systems (ICSPCS)
9581:
8753:
5664:
3849:
835:
748:
693:
293:
285:
208:
9817:
9335:{\displaystyle {\frac {1}{n}}\sum _{x,y}{\frac {1}{\sigma _{f}\sigma _{t}}}f(x,y)t(x,y)}
6501:{\displaystyle \operatorname {K} _{XY}(t_{1},t_{2})\triangleq \ \operatorname {E} \left}
6214:{\displaystyle \operatorname {R} _{XY}(t_{1},t_{2})\triangleq \ \operatorname {E} \left}
742:; however, this terminology is not used in probability and statistics. In contrast, the
12152:
11963:
11817:
11713:
11662:
11538:
11435:
11419:
11396:
11173:
10907:
10890:
10850:
10761:
10656:
10618:
10589:
10549:
10509:
10455:
10372:
10058:
10053:
9829:
9669:
9603:
9415:
9198:
9178:
9158:
9138:
9118:
9098:
9078:
9034:
8732:
8726:
8681:
8564:
8328:
7220:
6567:
6563:
6025:
6005:
5823:
5756:
5736:
4248:
4228:
4208:
4188:
4168:
4148:
4009:
3686:
3666:
3617:
3599:
3255:
3156:
3132:
3112:
3040:
3020:
3000:
2980:
2960:
1597:
1482:
1462:
1442:
1399:
1376:
1330:
1310:
1290:
1250:
1230:
889:
869:
673:
653:
623:
603:
431:
270:
9847:
9463:
9040:
7701:
1545:
12147:
12058:
12028:
12020:
11840:
11831:
11687:
11543:
11528:
11503:
11391:
11332:
11198:
11186:
10812:
10729:
10673:
10596:
10440:
10362:
10141:
10015:
9781:
9739:
9697:
9659:
9626:
9521:
9488:
9410:
9219:
6253:
Subtracting the mean before multiplication yields the cross-covariance between times
5107:
3976:
3150:
1167:
262:
181:
65:
9833:
9673:
12083:
12038:
11802:
11789:
11682:
11657:
11591:
11523:
11401:
11009:
10902:
10835:
10748:
10695:
10514:
10385:
10179:
10063:
9978:
9945:
9821:
9731:
9651:
9607:
9593:
9560:
9550:
9420:
9395:
7734:
5684:
4135:
2906:
2083:{\displaystyle (f\star g)\ \triangleq \sum _{m=-\infty }^{\infty }{\overline {f}}g}
1973:{\displaystyle (f\star g)\ \triangleq \sum _{m=-\infty }^{\infty }{\overline {f}}g}
6914:{\displaystyle \operatorname {K} _{XY}(\tau )\triangleq \ \operatorname {E} \left}
6671:{\displaystyle \operatorname {R} _{XY}(\tau )\triangleq \ \operatorname {E} \left}
12000:
11744:
11606:
11533:
11208:
11082:
11055:
11032:
11001:
10628:
10623:
10577:
10307:
9958:
9725:
9360:
5786:
3099:
644:
313:
305:
190:
11490:
9655:
9462:
Weisstein, Eric W. "Cross-Correlation." From MathWorld--A Wolfram Web
Resource.
8957:{\displaystyle \left\langle {\frac {F}{\|F\|}},{\frac {T}{\|T\|}}\right\rangle }
11949:
11944:
10407:
10337:
9983:
9400:
9365:
7214:
6242:
4488:
4484:
9825:
3180:, lagged cross-correlation is sometimes referred to as cross-autocorrelation.
3093:
12192:
12106:
12073:
11936:
11897:
11708:
11677:
11141:
11095:
10700:
10402:
10229:
9993:
9988:
9598:
8997:
7321:
The definition of the normalized cross-correlation of a stochastic process is
5778:
4361:
301:
9735:
9483:. Signal Processing Series. Upper Saddle River, NJ: Prentice Hall. pp.
5086:
need not have the same dimension, and either might be a scalar value. Where
2603:{\displaystyle (f\star g)\ \triangleq \sum _{m=0}^{N-1}{\overline {f}}K_{g}}
716:
is formally given by the cross-correlation (in the signal-processing sense)
12048:
11981:
11958:
11873:
11203:
10499:
10397:
10332:
10274:
10259:
10196:
10151:
9555:
3177:
6511:
12091:
12053:
11736:
11637:
11499:
11312:
11279:
10771:
10688:
10683:
10327:
10284:
10264:
10244:
10234:
10003:
9592:. Association for the Advancement of Artificial Intelligence: 4179â4186.
9545:(Doctoral thesis). Nanyang Technological University, Singapore. pp.
9380:
9375:
8757:
7740:
For jointly wide-sense stationary stochastic processes, the definition is
5782:
3249:
743:
501:
320:
309:
276:
186:
9565:
2898:{\displaystyle T_{i}(\cdot )\colon \mathbb {C} ^{M}\to \mathbb {C} ^{M}}
2392:{\displaystyle (f\star g)\ \triangleq \sum _{m=0}^{N-1}{\overline {f}}g}
2258:{\displaystyle (f\star g)\ \triangleq \sum _{m=0}^{N-1}{\overline {f}}g}
10937:
10417:
10117:
10048:
9998:
9973:
9893:
5680:
1870:
Similarly, for discrete functions, the cross-correlation is defined as:
324:
23:
9760:
9694:
Probability and Random
Processes for Electrical and Computer Engineers
9546:
7314:) to normalize the cross-correlation function to get a time-dependent
7148:, which are constant over time due to stationarity; and similarly for
7054:{\displaystyle \operatorname {K} _{XY}(\tau )=\operatorname {E} \left}
6765:{\displaystyle \operatorname {R} _{XY}(\tau )=\operatorname {E} \left}
11090:
10942:
10562:
10357:
10269:
10254:
10249:
10214:
7217:. That the cross-covariance and cross-correlation are independent of
297:
10606:
10224:
10101:
10096:
10091:
9027:
4492:
7733:, with 1 indicating perfect correlation and â1 indicating perfect
38:
12111:
11812:
8195:
5774:
9588:. The Thirty-second AAAI Conference On Artificial Intelligence.
12033:
11014:
10988:
10968:
10219:
10010:
7310:
It is common practice in some disciplines (e.g. statistics and
4330:{\displaystyle g\star \left(f*h\right)=\left(g\star f\right)*h}
690:, respectively, then the probability density of the difference
130:
500:
is a scalar random variable which is realized repeatedly in a
95:
9862:
9645:
9586:
Proceedings of the AAAI Conference on
Artificial Intelligence
6042:. Then the definition of the cross-correlation between times
5274:{\displaystyle \operatorname {R} _{\mathbf {X} \mathbf {Y} }}
861:
504:, then the correlations of the various temporal instances of
9858:
http://www.staff.ncl.ac.uk/oliver.hinton/eee305/Chapter6.pdf
5670:
9953:
8317:
5182:{\displaystyle \mathbf {X} =\left(X_{1},X_{2},X_{3}\right)}
9728:
Microphone Array
Analysis Methods Using Cross-Correlations
9803:
9762:
Real Time Implementation of a Military Impulse Classifier
9580:
Wang, Chen; Zhang, Le; Yuan, Junsong; Xie, Lihua (2018).
6574:
and the cross-correlation function are given as follows.
3017:
must be shifted along the x-axis to make it identical to
8756:
terms, this can be thought of as the dot product of two
6245:
operator. Note that this expression may be not defined.
5391:
9853:
http://scribblethink.org/Work/nvisionInterface/nip.html
6512:
Definition for wide-sense stationary stochastic process
1267:
which have a maximum cross-correlation at a particular
9218:
Normalized correlation is one of the methods used for
4667:
4344:
9240:
9229:
9201:
9181:
9161:
9141:
9121:
9101:
9081:
9043:
9006:
8970:
8904:
8835:
8766:
8735:
8704:
8684:
8657:
8622:
8587:
8567:
8410:
8372:
8337:
8208:
8103:
7984:
7746:
7704:
7674:
7327:
7243:
7223:
7187:
7154:
7121:
7094:
7067:
6927:
6784:
6684:
6587:
6522:
6313:
6286:
6259:
6227:
6102:
6075:
6048:
6028:
6008:
5967:
5926:
5890:
5854:
5826:
5795:
5759:
5739:
5693:
5641:
5570:
5548:
5526:
5462:
5402:
5345:
5313:
5287:
5253:
5240:{\displaystyle \mathbf {Y} =\left(Y_{1},Y_{2}\right)}
5195:
5124:
5092:
5070:
5048:
4641:
4615:
4549:
4527:
4505:
4429:
4369:
4273:
4251:
4231:
4211:
4191:
4171:
4151:
4032:
4012:
3985:
3957:
3859:
3749:
3709:
3689:
3669:
3626:
3602:
3472:
3350:
3319:
3278:
3258:
3225:
3196:
3159:
3135:
3115:
3063:
3043:
3023:
3003:
2983:
2963:
2918:
2845:
2772:
2616:
2475:
2440:
2405:
2271:
2137:
2096:
1986:
1876:
1748:
1620:
1600:
1548:
1528:
1505:
1485:
1465:
1445:
1422:
1402:
1379:
1353:
1333:
1313:
1293:
1273:
1253:
1233:
1205:
1176:
1134:
1023:
912:
892:
872:
838:
806:
777:
751:
722:
696:
676:
656:
626:
606:
580:
558:
536:
510:
484:
462:
440:
414:
392:
366:
344:
237:
211:
11775:
Autoregressive conditional heteroskedasticity (ARCH)
9543:
Kernel learning for visual perception, Chapter 2.2.1
832:) gives the probability density function of the sum
308:. The cross-correlation is similar in nature to the
9620:
9512:
Theory and Application of Digital Signal Processing
9464:
http://mathworld.wolfram.com/Cross-Correlation.html
7115:are the mean and standard deviation of the process
11237:
9509:
9476:
9334:
9207:
9187:
9167:
9147:
9127:
9107:
9087:
9064:
9018:
8988:
8956:
8890:
8821:
8741:
8717:
8690:
8670:
8643:
8608:
8573:
8550:
8393:
8358:
8306:
8171:
8089:
7953:
7725:
7690:
7660:
7275:
7229:
7205:
7173:
7140:
7107:
7080:
7053:
6913:
6764:
6670:
6554:
6500:
6299:
6272:
6233:
6213:
6088:
6061:
6034:
6014:
5994:
5953:
5912:
5876:
5832:
5808:
5765:
5745:
5725:
5655:
5627:
5556:
5534:
5509:{\displaystyle \mathbf {W} =(W_{1},\ldots ,W_{n})}
5508:
5449:{\displaystyle \mathbf {Z} =(Z_{1},\ldots ,Z_{m})}
5448:
5380:
5331:
5299:
5273:
5239:
5181:
5098:
5078:
5056:
5034:
4627:
4601:
4535:
4513:
4476:{\displaystyle \mathbf {Y} =(Y_{1},\ldots ,Y_{n})}
4475:
4416:{\displaystyle \mathbf {X} =(X_{1},\ldots ,X_{m})}
4415:
4329:
4257:
4237:
4217:
4197:
4177:
4157:
4115:
4018:
3998:
3967:
3942:
3837:
3733:
3695:
3675:
3653:
3608:
3586:
3455:
3334:
3305:
3264:
3240:
3211:
3165:
3141:
3121:
3081:
3049:
3029:
3009:
2989:
2969:
2957:As an example, consider two real valued functions
2940:
2897:
2831:
2758:
2602:
2461:
2426:
2391:
2257:
2123:
2082:
1972:
1862:
1734:
1606:
1586:
1534:
1514:
1491:
1471:
1451:
1428:
1408:
1385:
1365:
1339:
1319:
1299:
1279:
1259:
1239:
1211:
1191:
1158:
1120:
1009:
898:
878:
850:
824:
792:
763:
734:
708:
682:
662:
632:
612:
588:
566:
544:
518:
492:
470:
448:
422:
400:
374:
352:
249:
223:
7698:is well-defined, its value must lie in the range
5820:) produced by a given run of the process at time
2131:, the (circular) cross-correlation is defined as:
1479:are both continuous periodic functions of period
12190:
9579:
9516:. Englewood Cliffs, NJ: Prentice-Hall. pp.
8331:. That is, the cross-correlation of a template
11323:Multivariate adaptive regression splines (MARS)
6577:
4205:is the convolution of the cross-correlation of
9474:
9224:Pearson product-moment correlation coefficient
6774:
9878:
8989:{\displaystyle \langle \cdot ,\cdot \rangle }
5843:
2469:, the kernel cross-correlation is defined as:
1542:is replaced by integration over any interval
162:
9508:Rabiner, Lawrence R.; Gold, Bernard (1975).
9013:
9007:
8983:
8971:
8943:
8937:
8922:
8916:
6248:
408:are the correlations between the entries of
9507:
7290:The cross-correlation of a pair of jointly
9923:
9885:
9871:
4145:The cross-correlation of a convolution of
862:Cross-correlation of deterministic signals
169:
155:
10536:
9710:
9687:
9685:
9683:
9597:
9564:
9554:
8267:
8248:
5671:Cross-correlation of stochastic processes
4006:again indicates the complex conjugate of
2885:
2870:
2825:
2811:
2796:
2449:
2414:
2111:
1853:
1725:
1111:
1000:
193:. For the operations involving function
9775:
8318:Zero-normalized cross-correlation (ZNCC)
4134:The cross-correlation is related to the
3092:
771:(equivalent to the cross-correlation of
180:
8097:Respectively for jointly WSS processes:
2949:translation, rotation, and scale, etc.
2124:{\displaystyle f,g\in \mathbb {C} ^{N}}
12191:
11849:KaplanâMeier estimator (product limit)
9765:(MS thesis). University of Pittsburgh.
9691:
9680:
9037:then implies that ZNCC has a range of
8891:{\displaystyle T(x,y)=t(x,y)-\mu _{t}}
8822:{\displaystyle F(x,y)=f(x,y)-\mu _{f}}
8181:
906:, the cross-correlation is defined as:
11922:
11489:
11236:
10535:
10305:
9922:
9866:
9758:
9623:The Econometrics of Financial Markets
9475:Rabiner, L.R.; Schafer, R.W. (1978).
5683:, the cross-correlation of a pair of
5392:Definition for complex random vectors
3037:. The formula essentially slides the
2462:{\displaystyle g\in \mathbb {C} ^{M}}
2427:{\displaystyle f\in \mathbb {C} ^{N}}
12159:
11859:Accelerated failure time (AFT) model
9769:
9540:
9479:Digital Processing of Speech Signals
9344:
7973:
12171:
11454:Analysis of variance (ANOVA, anova)
10306:
5848:Suppose that the process has means
5733:be a pair of random processes, and
4345:Cross-correlation of random vectors
3306:{\displaystyle {\overline {f(-t)}}}
3190:The cross-correlation of functions
13:
11549:CochranâMantelâHaenszel statistics
10175:Pearson product-moment correlation
9797:
9639:
9625:. NJ: Princeton University Press.
9230:Normalized cross-correlation (NCC)
8255:
8252:
8249:
8245:
8242:
8239:
8227:
8224:
8221:
8218:
8215:
8136:
8105:
8037:
7986:
7831:
7776:
7484:
7377:
7206:{\displaystyle \operatorname {E} }
7188:
6956:
6929:
6816:
6786:
6713:
6686:
6619:
6589:
6365:
6315:
6234:{\displaystyle \operatorname {E} }
6228:
6154:
6104:
5995:{\displaystyle \sigma _{Y}^{2}(t)}
5954:{\displaystyle \sigma _{X}^{2}(t)}
5647:
5616:
5594:
5572:
5381:{\displaystyle \operatorname {E} }
5346:
5255:
5099:{\displaystyle \operatorname {E} }
5093:
4992:
4953:
4919:
4855:
4816:
4782:
4743:
4704:
4670:
4643:
4573:
4551:
4080:
4035:
3960:
3921:
3894:
3862:
3852:, the cross-correlation satisfies
2036:
2031:
1926:
1921:
1529:
1509:
1159:{\displaystyle {\overline {f(t)}}}
1067:
1062:
956:
951:
14:
12225:
9841:
9215:multiplied by a positive scalar.
3734:{\displaystyle f\star g=g\star f}
12170:
12158:
12146:
12133:
12132:
11923:
9848:Cross Correlation from Mathworld
9759:Rhudy, Matthew (November 2009).
9621:Campbell; Lo; MacKinlay (1996).
8314:Terminology in image processing
7305:
5610:
5604:
5582:
5577:
5550:
5528:
5464:
5404:
5265:
5260:
5197:
5126:
5072:
5050:
4653:
4648:
4590:
4585:
4561:
4556:
4529:
4507:
4431:
4371:
2766:is a vector of kernel functions
582:
560:
552:, and the cross-correlations of
538:
512:
486:
464:
442:
416:
394:
368:
346:
37:
11808:Least-squares spectral analysis
9752:
9719:
7968:
7316:Pearson correlation coefficient
3999:{\displaystyle {\overline {f}}}
10789:Mean-unbiased minimum-variance
9892:
9696:. Cambridge University Press.
9614:
9573:
9534:
9501:
9468:
9456:
9447:
9438:
9329:
9317:
9311:
9299:
9059:
9044:
8898:then the above sum is equal to
8872:
8860:
8851:
8839:
8803:
8791:
8782:
8770:
8638:
8626:
8603:
8591:
8527:
8515:
8486:
8474:
8388:
8376:
8353:
8341:
8301:
8298:
8292:
8289:
8277:
8274:
8160:
8151:
8126:
8120:
8078:
8052:
8027:
8001:
7797:
7791:
7766:
7760:
7720:
7705:
7652:
7639:
7626:
7613:
7472:
7459:
7446:
7433:
7418:
7392:
7367:
7341:
7270:
7244:
7200:
7194:
7168:
7155:
7135:
7122:
6950:
6944:
6807:
6801:
6707:
6701:
6610:
6604:
6549:
6523:
6484:
6481:
6468:
6435:
6424:
6411:
6356:
6330:
6145:
6119:
5989:
5983:
5948:
5942:
5907:
5901:
5871:
5865:
5720:
5694:
5622:
5600:
5503:
5471:
5443:
5411:
5375:
5352:
5326:
5314:
5021:
4998:
4982:
4959:
4948:
4925:
4884:
4861:
4845:
4822:
4811:
4788:
4772:
4749:
4733:
4710:
4699:
4676:
4470:
4438:
4410:
4378:
4099:
4093:
4059:
4050:
3968:{\displaystyle {\mathcal {F}}}
3578:
3569:
3566:
3557:
3551:
3533:
3527:
3518:
3512:
3506:
3503:
3500:
3494:
3485:
3479:
3473:
3447:
3441:
3438:
3435:
3429:
3414:
3405:
3396:
3390:
3384:
3381:
3378:
3372:
3363:
3357:
3351:
3329:
3323:
3294:
3285:
3235:
3229:
3206:
3200:
3076:
3064:
2952:
2935:
2929:
2880:
2862:
2856:
2821:
2788:
2776:
2753:
2750:
2747:
2741:
2716:
2701:
2698:
2692:
2673:
2664:
2661:
2655:
2636:
2630:
2597:
2580:
2567:
2564:
2545:
2539:
2497:
2491:
2488:
2476:
2399:For finite discrete functions
2386:
2380:
2368:
2351:
2338:
2335:
2293:
2287:
2284:
2272:
2252:
2235:
2222:
2219:
2207:
2201:
2159:
2153:
2150:
2138:
2090:For finite discrete functions
2077:
2071:
2059:
2047:
2008:
2002:
1999:
1987:
1967:
1955:
1943:
1937:
1898:
1892:
1889:
1877:
1850:
1844:
1832:
1820:
1770:
1764:
1761:
1749:
1722:
1710:
1698:
1692:
1642:
1636:
1633:
1621:
1581:
1549:
1186:
1180:
1147:
1141:
1108:
1102:
1090:
1078:
1045:
1039:
1036:
1024:
997:
985:
973:
967:
934:
928:
925:
913:
819:
810:
787:
781:
257:are identical in this example.
1:
12102:Geographic information system
11318:Simultaneous equations models
9432:
7276:{\displaystyle (X_{t},Y_{t})}
6568:jointly wide-sense stationary
6555:{\displaystyle (X_{t},Y_{t})}
5726:{\displaystyle (X_{t},Y_{t})}
4355:
3654:{\displaystyle f\star g=f*g.}
3183:
2941:{\displaystyle T_{i}(\cdot )}
649:probability density functions
197:, and assuming the height of
11285:Coefficient of determination
10896:Uniformly most powerful test
8164:
8082:
7916:
7591:
7041:
6901:
6752:
6658:
6488:
6201:
5656:{\displaystyle {}^{\rm {H}}}
5557:{\displaystyle \mathbf {W} }
5535:{\displaystyle \mathbf {Z} }
5079:{\displaystyle \mathbf {Y} }
5057:{\displaystyle \mathbf {X} }
4536:{\displaystyle \mathbf {Y} }
4514:{\displaystyle \mathbf {X} }
4108:
4063:
3991:
3911:
3561:
3537:
3418:
3298:
2549:
2372:
2211:
2063:
1947:
1836:
1702:
1151:
1094:
977:
589:{\displaystyle \mathbf {Y} }
567:{\displaystyle \mathbf {X} }
545:{\displaystyle \mathbf {X} }
519:{\displaystyle \mathbf {X} }
493:{\displaystyle \mathbf {Y} }
471:{\displaystyle \mathbf {X} }
449:{\displaystyle \mathbf {X} }
423:{\displaystyle \mathbf {X} }
401:{\displaystyle \mathbf {X} }
375:{\displaystyle \mathbf {Y} }
353:{\displaystyle \mathbf {X} }
7:
11854:Proportional hazards models
11798:Spectral density estimation
11780:Vector autoregression (VAR)
11214:Maximum posterior estimator
10446:Randomized controlled trial
9656:10.1109/ICSPCS.2015.7391783
9353:
8718:{\displaystyle \sigma _{f}}
8581:is the number of pixels in
7108:{\displaystyle \sigma _{X}}
5913:{\displaystyle \mu _{Y}(t)}
5877:{\displaystyle \mu _{X}(t)}
335:between the entries of two
10:
12230:
12204:Covariance and correlation
11614:Multivariate distributions
10034:Average absolute deviation
9019:{\displaystyle \|\cdot \|}
7691:{\displaystyle \rho _{XX}}
6578:Cross-correlation function
5844:Cross-correlation function
5113:
4348:
4129:circular cross-correlation
3082:{\displaystyle (f\star g)}
430:itself, those forming the
131:Cross-correlation function
96:Cross-correlation function
31:Correlation and covariance
16:Covariance and correlation
12128:
12082:
12019:
11972:
11935:
11931:
11918:
11890:
11872:
11839:
11830:
11788:
11735:
11696:
11645:
11636:
11602:Structural equation model
11557:
11514:
11510:
11485:
11444:
11410:
11364:
11331:
11293:
11260:
11256:
11232:
11172:
11081:
11000:
10964:
10955:
10938:Score/Lagrange multiplier
10923:
10876:
10821:
10747:
10738:
10548:
10544:
10531:
10490:
10464:
10416:
10371:
10353:Sample size determination
10318:
10314:
10301:
10205:
10160:
10134:
10116:
10072:
10024:
9944:
9935:
9931:
9918:
9900:
9826:10.1007/s10596-012-9287-1
9806:Computational Geosciences
9582:"Kernel Cross-Correlator"
9406:Digital image correlation
6775:Cross-covariance function
6572:cross-covariance function
6249:Cross-covariance function
5300:{\displaystyle 3\times 2}
5247:are random vectors, then
4635:. Written component-wise:
4628:{\displaystyle m\times n}
3587:{\displaystyle (t)=(-t).}
866:For continuous functions
312:of two functions. In an
141:Cross-covariance function
119:For deterministic signals
106:Cross-covariance function
12097:Environmental statistics
11619:Elliptical distributions
11412:Generalized linear model
11341:Simple linear regression
11111:HodgesâLehmann estimator
10568:Probability distribution
10477:Stochastic approximation
10039:Coefficient of variation
9776:Billings, S. A. (2013).
9692:Gubner, John A. (2006).
9599:10.1609/aaai.v32i1.11710
9391:Cross-correlation matrix
8671:{\displaystyle \mu _{f}}
7081:{\displaystyle \mu _{X}}
4497:cross-correlation matrix
4351:Cross-correlation matrix
3456:{\displaystyle (t)=(t).}
3108:complex-valued functions
1515:{\displaystyle -\infty }
735:{\displaystyle f\star g}
290:single particle analysis
250:{\displaystyle f\star g}
189:, cross-correlation and
126:Autocorrelation function
91:Autocorrelation function
84:For stochastic processes
61:Cross-correlation matrix
11757:Cross-correlation (XCF)
11365:Non-standard predictors
10799:LehmannâScheffĂŠ theorem
10472:Adaptive clinical trial
9736:10.1115/IMECE2009-10798
9426:WienerâKhinchin theorem
7287:wide-sense stationary.
7174:{\displaystyle (Y_{t})}
7141:{\displaystyle (X_{t})}
5665:Hermitian transposition
4140:WienerâKhinchin theorem
2265:which is equivalent to:
1980:which is equivalent to:
1535:{\displaystyle \infty }
1499:, the integration from
1366:{\displaystyle t+\tau }
136:Autocovariance function
101:Autocovariance function
71:Cross-covariance matrix
12153:Mathematics portal
11974:Engineering statistics
11882:NelsonâAalen estimator
11459:Analysis of covariance
11346:Ordinary least squares
11270:Pearson product-moment
10674:Statistical functional
10585:Empirical distribution
10418:Controlled experiments
10147:Frequency distribution
9925:Descriptive statistics
9336:
9209:
9189:
9169:
9149:
9129:
9109:
9089:
9066:
9020:
8990:
8958:
8892:
8823:
8743:
8719:
8692:
8672:
8645:
8644:{\displaystyle f(x,y)}
8610:
8609:{\displaystyle t(x,y)}
8575:
8552:
8395:
8394:{\displaystyle f(x,y)}
8360:
8359:{\displaystyle t(x,y)}
8308:
8173:
8091:
7963:statistical dependence
7955:
7727:
7692:
7662:
7277:
7231:
7207:
7175:
7142:
7109:
7082:
7055:
6915:
6766:
6672:
6556:
6502:
6301:
6274:
6235:
6215:
6090:
6063:
6036:
6016:
5996:
5955:
5914:
5878:
5834:
5810:
5767:
5753:be any point in time (
5747:
5727:
5657:
5629:
5558:
5536:
5518:complex random vectors
5510:
5450:
5382:
5333:
5301:
5275:
5241:
5183:
5100:
5080:
5058:
5036:
4629:
4603:
4537:
4515:
4477:
4417:
4331:
4259:
4239:
4219:
4199:
4179:
4159:
4125:fast Fourier transform
4117:
4020:
4000:
3969:
3944:
3839:
3735:
3697:
3677:
3655:
3610:
3588:
3457:
3336:
3307:
3266:
3242:
3213:
3167:
3143:
3123:
3103:
3083:
3051:
3031:
3011:
2991:
2971:
2942:
2899:
2833:
2760:
2759:{\displaystyle K_{g}=}
2604:
2532:
2463:
2428:
2393:
2328:
2259:
2194:
2125:
2084:
2040:
1974:
1930:
1864:
1742:which is equivalent to
1736:
1608:
1588:
1536:
1516:
1493:
1473:
1453:
1430:
1410:
1393:could be described to
1387:
1367:
1341:
1321:
1301:
1281:
1261:
1241:
1227:For highly-correlated
1213:
1193:
1160:
1122:
1017:which is equivalent to
1011:
900:
880:
852:
826:
794:
765:
736:
710:
684:
664:
634:
614:
590:
568:
546:
520:
494:
472:
450:
424:
402:
376:
354:
258:
251:
225:
66:Auto-covariance matrix
56:Autocorrelation matrix
12069:Population statistics
12011:System identification
11745:Autocorrelation (ACF)
11673:Exponential smoothing
11587:Discriminant analysis
11582:Canonical correlation
11446:Partition of variance
11308:Regression validation
11152:(JonckheereâTerpstra)
11051:Likelihood-ratio test
10740:Frequentist inference
10652:Locationâscale family
10573:Sampling distribution
10538:Statistical inference
10505:Cross-sectional study
10492:Observational studies
10451:Randomized experiment
10280:Stem-and-leaf display
10082:Central limit theorem
9337:
9210:
9190:
9170:
9150:
9130:
9110:
9090:
9067:
9021:
8991:
8959:
8893:
8824:
8744:
8720:
8693:
8673:
8646:
8611:
8576:
8553:
8396:
8361:
8309:
8174:
8092:
7956:
7728:
7693:
7663:
7292:wide sense stationary
7278:
7232:
7208:
7176:
7143:
7110:
7083:
7056:
6916:
6767:
6673:
6557:
6503:
6302:
6300:{\displaystyle t_{2}}
6275:
6273:{\displaystyle t_{1}}
6236:
6216:
6091:
6089:{\displaystyle t_{2}}
6064:
6062:{\displaystyle t_{1}}
6037:
6017:
5997:
5956:
5915:
5879:
5835:
5811:
5809:{\displaystyle X_{t}}
5768:
5748:
5728:
5658:
5630:
5559:
5537:
5511:
5451:
5383:
5334:
5332:{\displaystyle (i,j)}
5302:
5276:
5242:
5184:
5101:
5081:
5059:
5037:
4630:
4604:
4538:
4516:
4478:
4418:
4332:
4260:
4240:
4220:
4200:
4180:
4160:
4118:
4021:
4001:
3970:
3945:
3840:
3736:
3698:
3678:
3656:
3611:
3589:
3458:
3337:
3308:
3267:
3248:is equivalent to the
3243:
3214:
3168:
3144:
3124:
3096:
3084:
3052:
3032:
3012:
2992:
2972:
2943:
2900:
2834:
2761:
2605:
2506:
2464:
2429:
2394:
2302:
2260:
2168:
2126:
2085:
2017:
1975:
1907:
1865:
1737:
1609:
1589:
1537:
1517:
1494:
1474:
1454:
1431:
1429:{\displaystyle \tau }
1411:
1388:
1368:
1342:
1327:also occurs later in
1322:
1302:
1282:
1280:{\displaystyle \tau }
1262:
1242:
1214:
1212:{\displaystyle \tau }
1194:
1161:
1123:
1012:
901:
881:
853:
827:
825:{\displaystyle g(-t)}
795:
766:
737:
711:
685:
665:
635:
615:
591:
569:
547:
521:
495:
473:
451:
425:
403:
377:
355:
282:sliding inner-product
271:measure of similarity
252:
226:
185:Visual comparison of
184:
12214:Time domain analysis
11992:Probabilistic design
11577:Principal components
11420:Exponential families
11372:Nonlinear regression
11351:General linear model
11313:Mixed effects models
11303:Errors and residuals
11280:Confounding variable
11182:Bayesian probability
11160:Van der Waerden test
11150:Ordered alternative
10915:Multiple comparisons
10794:RaoâBlackwellization
10757:Estimating equations
10713:Statistical distance
10431:Factorial experiment
9964:Arithmetic-Geometric
9556:10.32657/10220/47835
9386:Correlation function
9238:
9199:
9179:
9159:
9139:
9119:
9099:
9079:
9041:
9004:
8968:
8902:
8833:
8764:
8733:
8702:
8682:
8655:
8620:
8585:
8565:
8408:
8370:
8335:
8206:
8101:
7982:
7744:
7702:
7672:
7325:
7312:time series analysis
7295:stochastic processes
7241:
7221:
7185:
7152:
7119:
7092:
7065:
6925:
6782:
6682:
6585:
6564:stochastic processes
6562:represent a pair of
6520:
6311:
6284:
6257:
6225:
6100:
6073:
6046:
6026:
6006:
5965:
5924:
5888:
5852:
5824:
5793:
5757:
5737:
5691:
5677:time series analysis
5639:
5568:
5546:
5524:
5460:
5400:
5343:
5311:
5285:
5251:
5193:
5122:
5090:
5068:
5046:
4639:
4613:
4547:
4525:
4503:
4427:
4367:
4271:
4249:
4229:
4209:
4189:
4169:
4149:
4030:
4010:
3983:
3955:
3857:
3747:
3707:
3703:are Hermitian, then
3687:
3667:
3624:
3600:
3470:
3348:
3335:{\displaystyle g(t)}
3317:
3276:
3256:
3241:{\displaystyle g(t)}
3223:
3212:{\displaystyle f(t)}
3194:
3157:
3133:
3113:
3061:
3041:
3021:
3001:
2981:
2961:
2916:
2843:
2770:
2614:
2473:
2438:
2403:
2269:
2135:
2094:
1984:
1874:
1746:
1618:
1598:
1546:
1526:
1503:
1483:
1463:
1443:
1420:
1400:
1377:
1351:
1331:
1311:
1291:
1271:
1251:
1231:
1203:
1192:{\displaystyle f(t)}
1174:
1132:
1021:
910:
890:
870:
836:
804:
793:{\displaystyle f(t)}
775:
749:
720:
694:
674:
654:
624:
604:
578:
556:
534:
508:
482:
460:
438:
412:
390:
364:
342:
235:
209:
22:Part of a series on
12064:Official statistics
11987:Methods engineering
11668:Seasonal adjustment
11436:Poisson regressions
11356:Bayesian regression
11295:Regression analysis
11275:Partial correlation
11247:Regression analysis
10846:Prediction interval
10841:Likelihood interval
10831:Confidence interval
10823:Interval estimation
10784:Unbiased estimators
10602:Model specification
10482:Up-and-down designs
10170:Partial correlation
10126:Index of dispersion
10044:Interquartile range
9818:2012CmpGe..16..779T
9541:Wang, Chen (2019).
8754:functional analysis
8182:Time delay analysis
5982:
5941:
5042:The random vectors
4609:and has dimensions
3850:convolution theorem
1813:
1685:
1071:
960:
851:{\displaystyle X+Y}
764:{\displaystyle f*g}
709:{\displaystyle Y-X}
386:of a random vector
294:electron tomography
286:pattern recognition
224:{\displaystyle f*g}
12084:Spatial statistics
11964:Medical statistics
11864:First hitting time
11818:Whittle likelihood
11469:Degrees of freedom
11464:Multivariate ANOVA
11397:Heteroscedasticity
11209:Bayesian estimator
11174:Bayesian inference
11023:KolmogorovâSmirnov
10908:Randomization test
10878:Testing hypotheses
10851:Tolerance interval
10762:Maximum likelihood
10657:Exponential family
10590:Density estimation
10550:Statistical theory
10510:Natural experiment
10456:Scientific control
10373:Survey methodology
10059:Standard deviation
9416:Scaled correlation
9332:
9266:
9205:
9185:
9165:
9145:
9125:
9105:
9085:
9062:
9016:
8986:
8954:
8888:
8819:
8758:normalized vectors
8739:
8727:standard deviation
8715:
8688:
8678:is the average of
8668:
8641:
8606:
8571:
8548:
8436:
8391:
8356:
8329:standard deviation
8304:
8272:
8187:Cross-correlations
8169:
8087:
7951:
7723:
7688:
7658:
7273:
7227:
7203:
7171:
7138:
7105:
7078:
7051:
6911:
6762:
6668:
6552:
6498:
6297:
6270:
6231:
6211:
6086:
6059:
6032:
6012:
5992:
5968:
5951:
5927:
5910:
5874:
5830:
5806:
5763:
5743:
5723:
5653:
5625:
5554:
5532:
5506:
5446:
5378:
5329:
5297:
5271:
5237:
5179:
5096:
5076:
5054:
5032:
5026:
4625:
4599:
4533:
4511:
4483:, each containing
4473:
4413:
4327:
4255:
4235:
4215:
4195:
4175:
4155:
4113:
4016:
3996:
3965:
3940:
3835:
3731:
3693:
3673:
3651:
3618:Hermitian function
3606:
3584:
3453:
3332:
3303:
3262:
3238:
3209:
3163:
3139:
3119:
3104:
3079:
3047:
3027:
3007:
2987:
2967:
2938:
2895:
2829:
2756:
2600:
2459:
2424:
2389:
2255:
2121:
2080:
1970:
1860:
1779:
1732:
1651:
1604:
1584:
1532:
1512:
1489:
1469:
1449:
1426:
1406:
1383:
1363:
1337:
1317:
1297:
1277:
1257:
1237:
1209:
1189:
1156:
1118:
1054:
1007:
943:
896:
876:
848:
822:
790:
761:
732:
706:
680:
660:
630:
610:
586:
564:
542:
516:
490:
468:
446:
432:correlation matrix
420:
398:
372:
350:
329:cross-correlations
259:
247:
221:
49:For random vectors
12209:Signal processing
12186:
12185:
12124:
12123:
12120:
12119:
12059:National accounts
12029:Actuarial science
12021:Social statistics
11914:
11913:
11910:
11909:
11906:
11905:
11841:Survival function
11826:
11825:
11688:Granger causality
11529:Contingency table
11504:Survival analysis
11481:
11480:
11477:
11476:
11333:Linear regression
11228:
11227:
11224:
11223:
11199:Credible interval
11168:
11167:
10951:
10950:
10767:Method of moments
10636:Parametric family
10597:Statistical model
10527:
10526:
10523:
10522:
10441:Random assignment
10363:Statistical power
10297:
10296:
10293:
10292:
10142:Contingency table
10112:
10111:
9979:Generalized/power
9787:978-1-118-53556-1
9745:978-0-7918-4388-8
9703:978-0-521-86470-1
9665:978-1-4673-8118-5
9411:Phase correlation
9345:Nonlinear systems
9294:
9251:
9249:
9220:template matching
9208:{\displaystyle T}
9188:{\displaystyle F}
9168:{\displaystyle 1}
9148:{\displaystyle T}
9128:{\displaystyle F}
9108:{\displaystyle t}
9088:{\displaystyle f}
8947:
8926:
8742:{\displaystyle f}
8691:{\displaystyle f}
8574:{\displaystyle n}
8464:
8421:
8419:
8237:
8200:cross-correlation
8191:cross-correlation
8167:
8085:
7974:Symmetry property
7949:
7919:
7823:
7656:
7594:
7476:
7230:{\displaystyle t}
7199:
7044:
6904:
6815:
6755:
6661:
6618:
6491:
6364:
6204:
6153:
6035:{\displaystyle t}
6015:{\displaystyle t}
5833:{\displaystyle t}
5816:is the value (or
5766:{\displaystyle t}
5746:{\displaystyle t}
5593:
5108:expectation value
4572:
4258:{\displaystyle h}
4238:{\displaystyle f}
4218:{\displaystyle g}
4198:{\displaystyle g}
4178:{\displaystyle h}
4158:{\displaystyle f}
4111:
4066:
4019:{\displaystyle f}
3994:
3977:Fourier transform
3914:
3848:Analogous to the
3696:{\displaystyle g}
3676:{\displaystyle f}
3609:{\displaystyle f}
3564:
3540:
3421:
3301:
3265:{\displaystyle *}
3166:{\displaystyle f}
3142:{\displaystyle g}
3122:{\displaystyle f}
3050:{\displaystyle g}
3030:{\displaystyle f}
3010:{\displaystyle g}
2990:{\displaystyle g}
2970:{\displaystyle f}
2591:
2587:
2552:
2502:
2375:
2362:
2358:
2298:
2246:
2242:
2214:
2164:
2066:
2013:
1950:
1903:
1839:
1775:
1705:
1647:
1607:{\displaystyle T}
1492:{\displaystyle T}
1472:{\displaystyle g}
1452:{\displaystyle f}
1409:{\displaystyle f}
1386:{\displaystyle g}
1340:{\displaystyle g}
1320:{\displaystyle t}
1300:{\displaystyle f}
1260:{\displaystyle g}
1240:{\displaystyle f}
1168:complex conjugate
1154:
1097:
1050:
980:
939:
899:{\displaystyle g}
879:{\displaystyle f}
683:{\displaystyle g}
663:{\displaystyle f}
633:{\displaystyle Y}
613:{\displaystyle X}
267:cross-correlation
263:signal processing
179:
178:
12221:
12174:
12173:
12162:
12161:
12151:
12150:
12136:
12135:
12039:Crime statistics
11933:
11932:
11920:
11919:
11837:
11836:
11803:Fourier analysis
11790:Frequency domain
11770:
11717:
11683:Structural break
11643:
11642:
11592:Cluster analysis
11539:Log-linear model
11512:
11511:
11487:
11486:
11428:
11402:Homoscedasticity
11258:
11257:
11234:
11233:
11153:
11145:
11137:
11136:(KruskalâWallis)
11121:
11106:
11061:Cross validation
11046:
11028:AndersonâDarling
10975:
10962:
10961:
10933:Likelihood-ratio
10925:Parametric tests
10903:Permutation test
10886:1- & 2-tails
10777:Minimum distance
10749:Point estimation
10745:
10744:
10696:Optimal decision
10647:
10546:
10545:
10533:
10532:
10515:Quasi-experiment
10465:Adaptive designs
10316:
10315:
10303:
10302:
10180:Rank correlation
9942:
9941:
9933:
9932:
9920:
9919:
9887:
9880:
9873:
9864:
9863:
9837:
9792:
9791:
9773:
9767:
9766:
9756:
9750:
9749:
9723:
9717:
9714:
9708:
9707:
9689:
9678:
9677:
9650:. pp. 1â6.
9643:
9637:
9636:
9618:
9612:
9611:
9601:
9577:
9571:
9570:
9568:
9558:
9538:
9532:
9531:
9515:
9505:
9499:
9498:
9482:
9472:
9466:
9460:
9454:
9451:
9445:
9442:
9421:Spectral density
9396:Cross-covariance
9341:
9339:
9338:
9333:
9295:
9293:
9292:
9291:
9282:
9281:
9268:
9265:
9250:
9242:
9214:
9212:
9211:
9206:
9194:
9192:
9191:
9186:
9174:
9172:
9171:
9166:
9154:
9152:
9151:
9146:
9134:
9132:
9131:
9126:
9114:
9112:
9111:
9106:
9094:
9092:
9091:
9086:
9071:
9069:
9068:
9065:{\displaystyle }
9063:
9025:
9023:
9022:
9017:
8995:
8993:
8992:
8987:
8963:
8961:
8960:
8955:
8953:
8949:
8948:
8946:
8932:
8927:
8925:
8911:
8897:
8895:
8894:
8889:
8887:
8886:
8828:
8826:
8825:
8820:
8818:
8817:
8748:
8746:
8745:
8740:
8724:
8722:
8721:
8716:
8714:
8713:
8697:
8695:
8694:
8689:
8677:
8675:
8674:
8669:
8667:
8666:
8650:
8648:
8647:
8642:
8615:
8613:
8612:
8607:
8580:
8578:
8577:
8572:
8557:
8555:
8554:
8549:
8547:
8543:
8542:
8541:
8506:
8502:
8501:
8500:
8465:
8463:
8462:
8461:
8452:
8451:
8438:
8435:
8420:
8412:
8400:
8398:
8397:
8392:
8366:with a subimage
8365:
8363:
8362:
8357:
8324:image-processing
8313:
8311:
8310:
8305:
8273:
8271:
8270:
8258:
8232:
8231:
8230:
8178:
8176:
8175:
8170:
8168:
8163:
8147:
8146:
8133:
8116:
8115:
8096:
8094:
8093:
8088:
8086:
8081:
8077:
8076:
8064:
8063:
8048:
8047:
8034:
8026:
8025:
8013:
8012:
7997:
7996:
7960:
7958:
7957:
7952:
7950:
7948:
7947:
7946:
7937:
7936:
7926:
7925:
7921:
7920:
7915:
7911:
7910:
7909:
7897:
7896:
7876:
7874:
7870:
7869:
7868:
7856:
7855:
7829:
7824:
7822:
7821:
7820:
7811:
7810:
7800:
7787:
7786:
7773:
7759:
7758:
7735:anti-correlation
7732:
7730:
7729:
7726:{\displaystyle }
7724:
7697:
7695:
7694:
7689:
7687:
7686:
7668:If the function
7667:
7665:
7664:
7659:
7657:
7655:
7651:
7650:
7638:
7637:
7625:
7624:
7612:
7611:
7601:
7600:
7596:
7595:
7590:
7586:
7585:
7584:
7583:
7582:
7565:
7564:
7563:
7562:
7543:
7541:
7537:
7536:
7535:
7534:
7533:
7516:
7515:
7514:
7513:
7482:
7477:
7475:
7471:
7470:
7458:
7457:
7445:
7444:
7432:
7431:
7421:
7417:
7416:
7404:
7403:
7388:
7387:
7374:
7366:
7365:
7353:
7352:
7340:
7339:
7282:
7280:
7279:
7274:
7269:
7268:
7256:
7255:
7236:
7234:
7233:
7228:
7212:
7210:
7209:
7204:
7197:
7181:, respectively.
7180:
7178:
7177:
7172:
7167:
7166:
7147:
7145:
7144:
7139:
7134:
7133:
7114:
7112:
7111:
7106:
7104:
7103:
7087:
7085:
7084:
7079:
7077:
7076:
7060:
7058:
7057:
7052:
7050:
7046:
7045:
7040:
7036:
7035:
7034:
7022:
7021:
7007:
7005:
7001:
7000:
6999:
6987:
6986:
6940:
6939:
6921:or equivalently
6920:
6918:
6917:
6912:
6910:
6906:
6905:
6900:
6896:
6895:
6894:
6882:
6881:
6861:
6859:
6855:
6854:
6853:
6841:
6840:
6813:
6797:
6796:
6771:
6769:
6768:
6763:
6761:
6757:
6756:
6751:
6750:
6741:
6739:
6738:
6697:
6696:
6678:or equivalently
6677:
6675:
6674:
6669:
6667:
6663:
6662:
6657:
6656:
6641:
6639:
6638:
6616:
6600:
6599:
6561:
6559:
6558:
6553:
6548:
6547:
6535:
6534:
6507:
6505:
6504:
6499:
6497:
6493:
6492:
6487:
6480:
6479:
6467:
6466:
6454:
6453:
6452:
6451:
6433:
6431:
6427:
6423:
6422:
6410:
6409:
6397:
6396:
6395:
6394:
6362:
6355:
6354:
6342:
6341:
6326:
6325:
6306:
6304:
6303:
6298:
6296:
6295:
6279:
6277:
6276:
6271:
6269:
6268:
6240:
6238:
6237:
6232:
6220:
6218:
6217:
6212:
6210:
6206:
6205:
6200:
6199:
6198:
6197:
6183:
6181:
6180:
6179:
6178:
6151:
6144:
6143:
6131:
6130:
6115:
6114:
6095:
6093:
6092:
6087:
6085:
6084:
6068:
6066:
6065:
6060:
6058:
6057:
6041:
6039:
6038:
6033:
6021:
6019:
6018:
6013:
6001:
5999:
5998:
5993:
5981:
5976:
5960:
5958:
5957:
5952:
5940:
5935:
5919:
5917:
5916:
5911:
5900:
5899:
5883:
5881:
5880:
5875:
5864:
5863:
5839:
5837:
5836:
5831:
5815:
5813:
5812:
5807:
5805:
5804:
5772:
5770:
5769:
5764:
5752:
5750:
5749:
5744:
5732:
5730:
5729:
5724:
5719:
5718:
5706:
5705:
5662:
5660:
5659:
5654:
5652:
5651:
5650:
5644:
5634:
5632:
5631:
5626:
5621:
5620:
5619:
5613:
5607:
5591:
5587:
5586:
5585:
5580:
5563:
5561:
5560:
5555:
5553:
5541:
5539:
5538:
5533:
5531:
5515:
5513:
5512:
5507:
5502:
5501:
5483:
5482:
5467:
5455:
5453:
5452:
5447:
5442:
5441:
5423:
5422:
5407:
5387:
5385:
5384:
5379:
5374:
5373:
5364:
5363:
5338:
5336:
5335:
5330:
5306:
5304:
5303:
5298:
5280:
5278:
5277:
5272:
5270:
5269:
5268:
5263:
5246:
5244:
5243:
5238:
5236:
5232:
5231:
5230:
5218:
5217:
5200:
5188:
5186:
5185:
5180:
5178:
5174:
5173:
5172:
5160:
5159:
5147:
5146:
5129:
5118:For example, if
5105:
5103:
5102:
5097:
5085:
5083:
5082:
5077:
5075:
5063:
5061:
5060:
5055:
5053:
5041:
5039:
5038:
5033:
5031:
5030:
5020:
5019:
5010:
5009:
4981:
4980:
4971:
4970:
4947:
4946:
4937:
4936:
4915:
4890:
4883:
4882:
4873:
4872:
4844:
4843:
4834:
4833:
4810:
4809:
4800:
4799:
4778:
4771:
4770:
4761:
4760:
4732:
4731:
4722:
4721:
4698:
4697:
4688:
4687:
4658:
4657:
4656:
4651:
4634:
4632:
4631:
4626:
4608:
4606:
4605:
4600:
4598:
4594:
4593:
4588:
4570:
4566:
4565:
4564:
4559:
4542:
4540:
4539:
4534:
4532:
4520:
4518:
4517:
4512:
4510:
4482:
4480:
4479:
4474:
4469:
4468:
4450:
4449:
4434:
4422:
4420:
4419:
4414:
4409:
4408:
4390:
4389:
4374:
4336:
4334:
4333:
4328:
4320:
4316:
4298:
4294:
4264:
4262:
4261:
4256:
4245:with the kernel
4244:
4242:
4241:
4236:
4224:
4222:
4221:
4216:
4204:
4202:
4201:
4196:
4185:with a function
4184:
4182:
4181:
4176:
4164:
4162:
4161:
4156:
4136:spectral density
4122:
4120:
4119:
4114:
4112:
4107:
4106:
4102:
4084:
4083:
4076:
4071:
4067:
4062:
4045:
4039:
4038:
4025:
4023:
4022:
4017:
4005:
4003:
4002:
3997:
3995:
3987:
3974:
3972:
3971:
3966:
3964:
3963:
3949:
3947:
3946:
3941:
3936:
3925:
3924:
3915:
3910:
3909:
3898:
3897:
3890:
3885:
3881:
3866:
3865:
3844:
3842:
3841:
3836:
3834:
3830:
3812:
3808:
3790:
3786:
3768:
3764:
3740:
3738:
3737:
3732:
3702:
3700:
3699:
3694:
3682:
3680:
3679:
3674:
3660:
3658:
3657:
3652:
3615:
3613:
3612:
3607:
3593:
3591:
3590:
3585:
3565:
3560:
3546:
3541:
3536:
3522:
3462:
3460:
3459:
3454:
3422:
3417:
3400:
3341:
3339:
3338:
3333:
3312:
3310:
3309:
3304:
3302:
3297:
3280:
3271:
3269:
3268:
3263:
3247:
3245:
3244:
3239:
3218:
3216:
3215:
3210:
3172:
3170:
3169:
3164:
3148:
3146:
3145:
3140:
3128:
3126:
3125:
3120:
3088:
3086:
3085:
3080:
3056:
3054:
3053:
3048:
3036:
3034:
3033:
3028:
3016:
3014:
3013:
3008:
2996:
2994:
2993:
2988:
2976:
2974:
2973:
2968:
2947:
2945:
2944:
2939:
2928:
2927:
2907:affine transform
2904:
2902:
2901:
2896:
2894:
2893:
2888:
2879:
2878:
2873:
2855:
2854:
2838:
2836:
2835:
2830:
2828:
2820:
2819:
2814:
2805:
2804:
2799:
2765:
2763:
2762:
2757:
2740:
2739:
2691:
2690:
2654:
2653:
2626:
2625:
2609:
2607:
2606:
2601:
2596:
2595:
2589:
2588:
2585:
2563:
2562:
2553:
2548:
2534:
2531:
2520:
2500:
2468:
2466:
2465:
2460:
2458:
2457:
2452:
2433:
2431:
2430:
2425:
2423:
2422:
2417:
2398:
2396:
2395:
2390:
2376:
2371:
2367:
2366:
2360:
2359:
2356:
2330:
2327:
2316:
2296:
2264:
2262:
2261:
2256:
2251:
2250:
2244:
2243:
2240:
2215:
2210:
2196:
2193:
2182:
2162:
2130:
2128:
2127:
2122:
2120:
2119:
2114:
2089:
2087:
2086:
2081:
2067:
2062:
2042:
2039:
2034:
2011:
1979:
1977:
1976:
1971:
1951:
1946:
1932:
1929:
1924:
1901:
1869:
1867:
1866:
1861:
1840:
1835:
1815:
1812:
1805:
1804:
1794:
1793:
1792:
1773:
1741:
1739:
1738:
1733:
1706:
1701:
1687:
1684:
1677:
1676:
1666:
1665:
1664:
1645:
1613:
1611:
1610:
1605:
1593:
1591:
1590:
1587:{\displaystyle }
1585:
1574:
1573:
1561:
1560:
1541:
1539:
1538:
1533:
1521:
1519:
1518:
1513:
1498:
1496:
1495:
1490:
1478:
1476:
1475:
1470:
1458:
1456:
1455:
1450:
1435:
1433:
1432:
1427:
1415:
1413:
1412:
1407:
1392:
1390:
1389:
1384:
1372:
1370:
1369:
1364:
1346:
1344:
1343:
1338:
1326:
1324:
1323:
1318:
1306:
1304:
1303:
1298:
1286:
1284:
1283:
1278:
1266:
1264:
1263:
1258:
1246:
1244:
1243:
1238:
1218:
1216:
1215:
1210:
1198:
1196:
1195:
1190:
1165:
1163:
1162:
1157:
1155:
1150:
1136:
1127:
1125:
1124:
1119:
1098:
1093:
1073:
1070:
1065:
1048:
1016:
1014:
1013:
1008:
981:
976:
962:
959:
954:
937:
905:
903:
902:
897:
885:
883:
882:
877:
857:
855:
854:
849:
831:
829:
828:
823:
799:
797:
796:
791:
770:
768:
767:
762:
741:
739:
738:
733:
715:
713:
712:
707:
689:
687:
686:
681:
669:
667:
666:
661:
645:random variables
639:
637:
636:
631:
619:
617:
616:
611:
595:
593:
592:
587:
585:
573:
571:
570:
565:
563:
551:
549:
548:
543:
541:
528:autocorrelations
525:
523:
522:
517:
515:
499:
497:
496:
491:
489:
477:
475:
474:
469:
467:
455:
453:
452:
447:
445:
429:
427:
426:
421:
419:
407:
405:
404:
399:
397:
381:
379:
378:
373:
371:
359:
357:
356:
351:
349:
256:
254:
253:
248:
230:
228:
227:
222:
204:
200:
196:
171:
164:
157:
41:
19:
18:
12229:
12228:
12224:
12223:
12222:
12220:
12219:
12218:
12189:
12188:
12187:
12182:
12145:
12116:
12078:
12015:
12001:quality control
11968:
11950:Clinical trials
11927:
11902:
11886:
11874:Hazard function
11868:
11822:
11784:
11768:
11731:
11727:BreuschâGodfrey
11715:
11692:
11632:
11607:Factor analysis
11553:
11534:Graphical model
11506:
11473:
11440:
11426:
11406:
11360:
11327:
11289:
11252:
11251:
11220:
11164:
11151:
11143:
11135:
11119:
11104:
11083:Rank statistics
11077:
11056:Model selection
11044:
11002:Goodness of fit
10996:
10973:
10947:
10919:
10872:
10817:
10806:Median unbiased
10734:
10645:
10578:Order statistic
10540:
10519:
10486:
10460:
10412:
10367:
10310:
10308:Data collection
10289:
10201:
10156:
10130:
10108:
10068:
10020:
9937:Continuous data
9927:
9914:
9896:
9891:
9844:
9800:
9798:Further reading
9795:
9788:
9774:
9770:
9757:
9753:
9746:
9724:
9720:
9715:
9711:
9704:
9690:
9681:
9666:
9644:
9640:
9633:
9619:
9615:
9578:
9574:
9539:
9535:
9528:
9506:
9502:
9495:
9473:
9469:
9461:
9457:
9452:
9448:
9443:
9439:
9435:
9430:
9361:Autocorrelation
9356:
9347:
9287:
9283:
9277:
9273:
9272:
9267:
9255:
9241:
9239:
9236:
9235:
9232:
9200:
9197:
9196:
9180:
9177:
9176:
9175:if and only if
9160:
9157:
9156:
9140:
9137:
9136:
9120:
9117:
9116:
9100:
9097:
9096:
9080:
9077:
9076:
9042:
9039:
9038:
9005:
9002:
9001:
8969:
8966:
8965:
8936:
8931:
8915:
8910:
8909:
8905:
8903:
8900:
8899:
8882:
8878:
8834:
8831:
8830:
8813:
8809:
8765:
8762:
8761:
8734:
8731:
8730:
8709:
8705:
8703:
8700:
8699:
8683:
8680:
8679:
8662:
8658:
8656:
8653:
8652:
8621:
8618:
8617:
8586:
8583:
8582:
8566:
8563:
8562:
8560:
8537:
8533:
8511:
8507:
8496:
8492:
8470:
8466:
8457:
8453:
8447:
8443:
8442:
8437:
8425:
8411:
8409:
8406:
8405:
8404:
8371:
8368:
8367:
8336:
8333:
8332:
8320:
8266:
8259:
8238:
8236:
8214:
8213:
8209:
8207:
8204:
8203:
8184:
8139:
8135:
8134:
8132:
8108:
8104:
8102:
8099:
8098:
8072:
8068:
8059:
8055:
8040:
8036:
8035:
8033:
8021:
8017:
8008:
8004:
7989:
7985:
7983:
7980:
7979:
7976:
7971:
7942:
7938:
7932:
7928:
7927:
7905:
7901:
7886:
7882:
7881:
7877:
7875:
7864:
7860:
7851:
7847:
7846:
7842:
7841:
7837:
7830:
7828:
7816:
7812:
7806:
7802:
7801:
7779:
7775:
7774:
7772:
7751:
7747:
7745:
7742:
7741:
7703:
7700:
7699:
7679:
7675:
7673:
7670:
7669:
7646:
7642:
7633:
7629:
7620:
7616:
7607:
7603:
7602:
7578:
7574:
7573:
7569:
7558:
7554:
7553:
7549:
7548:
7544:
7542:
7529:
7525:
7524:
7520:
7509:
7505:
7504:
7500:
7499:
7495:
7494:
7490:
7483:
7481:
7466:
7462:
7453:
7449:
7440:
7436:
7427:
7423:
7422:
7412:
7408:
7399:
7395:
7380:
7376:
7375:
7373:
7361:
7357:
7348:
7344:
7332:
7328:
7326:
7323:
7322:
7308:
7264:
7260:
7251:
7247:
7242:
7239:
7238:
7222:
7219:
7218:
7186:
7183:
7182:
7162:
7158:
7153:
7150:
7149:
7129:
7125:
7120:
7117:
7116:
7099:
7095:
7093:
7090:
7089:
7072:
7068:
7066:
7063:
7062:
7030:
7026:
7017:
7013:
7012:
7008:
7006:
6995:
6991:
6976:
6972:
6971:
6967:
6966:
6962:
6932:
6928:
6926:
6923:
6922:
6890:
6886:
6871:
6867:
6866:
6862:
6860:
6849:
6845:
6836:
6832:
6831:
6827:
6826:
6822:
6789:
6785:
6783:
6780:
6779:
6777:
6746:
6742:
6740:
6728:
6724:
6723:
6719:
6689:
6685:
6683:
6680:
6679:
6646:
6642:
6640:
6634:
6630:
6629:
6625:
6592:
6588:
6586:
6583:
6582:
6580:
6543:
6539:
6530:
6526:
6521:
6518:
6517:
6514:
6475:
6471:
6462:
6458:
6447:
6443:
6442:
6438:
6434:
6432:
6418:
6414:
6405:
6401:
6390:
6386:
6385:
6381:
6380:
6376:
6375:
6371:
6350:
6346:
6337:
6333:
6318:
6314:
6312:
6309:
6308:
6291:
6287:
6285:
6282:
6281:
6264:
6260:
6258:
6255:
6254:
6251:
6226:
6223:
6222:
6193:
6189:
6188:
6184:
6182:
6174:
6170:
6169:
6165:
6164:
6160:
6139:
6135:
6126:
6122:
6107:
6103:
6101:
6098:
6097:
6080:
6076:
6074:
6071:
6070:
6053:
6049:
6047:
6044:
6043:
6027:
6024:
6023:
6007:
6004:
6003:
5977:
5972:
5966:
5963:
5962:
5936:
5931:
5925:
5922:
5921:
5895:
5891:
5889:
5886:
5885:
5859:
5855:
5853:
5850:
5849:
5846:
5825:
5822:
5821:
5800:
5796:
5794:
5791:
5790:
5789:process). Then
5787:continuous-time
5758:
5755:
5754:
5738:
5735:
5734:
5714:
5710:
5701:
5697:
5692:
5689:
5688:
5673:
5646:
5645:
5643:
5642:
5640:
5637:
5636:
5615:
5614:
5609:
5608:
5603:
5581:
5576:
5575:
5571:
5569:
5566:
5565:
5549:
5547:
5544:
5543:
5527:
5525:
5522:
5521:
5497:
5493:
5478:
5474:
5463:
5461:
5458:
5457:
5437:
5433:
5418:
5414:
5403:
5401:
5398:
5397:
5394:
5369:
5365:
5359:
5355:
5344:
5341:
5340:
5312:
5309:
5308:
5286:
5283:
5282:
5264:
5259:
5258:
5254:
5252:
5249:
5248:
5226:
5222:
5213:
5209:
5208:
5204:
5196:
5194:
5191:
5190:
5168:
5164:
5155:
5151:
5142:
5138:
5137:
5133:
5125:
5123:
5120:
5119:
5116:
5091:
5088:
5087:
5071:
5069:
5066:
5065:
5049:
5047:
5044:
5043:
5025:
5024:
5015:
5011:
5005:
5001:
4990:
4985:
4976:
4972:
4966:
4962:
4951:
4942:
4938:
4932:
4928:
4916:
4913:
4912:
4907:
4902:
4897:
4891:
4888:
4887:
4878:
4874:
4868:
4864:
4853:
4848:
4839:
4835:
4829:
4825:
4814:
4805:
4801:
4795:
4791:
4779:
4776:
4775:
4766:
4762:
4756:
4752:
4741:
4736:
4727:
4723:
4717:
4713:
4702:
4693:
4689:
4683:
4679:
4663:
4662:
4652:
4647:
4646:
4642:
4640:
4637:
4636:
4614:
4611:
4610:
4589:
4584:
4583:
4579:
4560:
4555:
4554:
4550:
4548:
4545:
4544:
4528:
4526:
4523:
4522:
4506:
4504:
4501:
4500:
4485:random elements
4464:
4460:
4445:
4441:
4430:
4428:
4425:
4424:
4404:
4400:
4385:
4381:
4370:
4368:
4365:
4364:
4358:
4353:
4347:
4342:
4306:
4302:
4284:
4280:
4272:
4269:
4268:
4250:
4247:
4246:
4230:
4227:
4226:
4210:
4207:
4206:
4190:
4187:
4186:
4170:
4167:
4166:
4150:
4147:
4146:
4123:. Coupled with
4089:
4085:
4079:
4078:
4077:
4075:
4046:
4044:
4040:
4034:
4033:
4031:
4028:
4027:
4011:
4008:
4007:
3986:
3984:
3981:
3980:
3959:
3958:
3956:
3953:
3952:
3926:
3920:
3919:
3899:
3893:
3892:
3891:
3889:
3871:
3867:
3861:
3860:
3858:
3855:
3854:
3820:
3816:
3798:
3794:
3776:
3772:
3754:
3750:
3748:
3745:
3744:
3708:
3705:
3704:
3688:
3685:
3684:
3668:
3665:
3664:
3625:
3622:
3621:
3601:
3598:
3597:
3547:
3545:
3523:
3521:
3471:
3468:
3467:
3401:
3399:
3349:
3346:
3345:
3318:
3315:
3314:
3281:
3279:
3277:
3274:
3273:
3257:
3254:
3253:
3224:
3221:
3220:
3195:
3192:
3191:
3186:
3158:
3155:
3154:
3134:
3131:
3130:
3114:
3111:
3110:
3100:Lissajous curve
3062:
3059:
3058:
3042:
3039:
3038:
3022:
3019:
3018:
3002:
2999:
2998:
2982:
2979:
2978:
2962:
2959:
2958:
2955:
2923:
2919:
2917:
2914:
2913:
2889:
2884:
2883:
2874:
2869:
2868:
2850:
2846:
2844:
2841:
2840:
2824:
2815:
2810:
2809:
2800:
2795:
2794:
2771:
2768:
2767:
2729:
2725:
2686:
2682:
2649:
2645:
2621:
2617:
2615:
2612:
2611:
2584:
2583:
2579:
2558:
2554:
2535:
2533:
2521:
2510:
2474:
2471:
2470:
2453:
2448:
2447:
2439:
2436:
2435:
2418:
2413:
2412:
2404:
2401:
2400:
2355:
2354:
2350:
2331:
2329:
2317:
2306:
2270:
2267:
2266:
2239:
2238:
2234:
2197:
2195:
2183:
2172:
2136:
2133:
2132:
2115:
2110:
2109:
2095:
2092:
2091:
2043:
2041:
2035:
2021:
1985:
1982:
1981:
1933:
1931:
1925:
1911:
1875:
1872:
1871:
1816:
1814:
1800:
1796:
1795:
1788:
1784:
1783:
1747:
1744:
1743:
1688:
1686:
1672:
1668:
1667:
1660:
1656:
1655:
1619:
1616:
1615:
1599:
1596:
1595:
1569:
1565:
1556:
1552:
1547:
1544:
1543:
1527:
1524:
1523:
1504:
1501:
1500:
1484:
1481:
1480:
1464:
1461:
1460:
1444:
1441:
1440:
1421:
1418:
1417:
1401:
1398:
1397:
1378:
1375:
1374:
1352:
1349:
1348:
1332:
1329:
1328:
1312:
1309:
1308:
1292:
1289:
1288:
1287:, a feature in
1272:
1269:
1268:
1252:
1249:
1248:
1232:
1229:
1228:
1204:
1201:
1200:
1175:
1172:
1171:
1137:
1135:
1133:
1130:
1129:
1074:
1072:
1066:
1058:
1022:
1019:
1018:
963:
961:
955:
947:
911:
908:
907:
891:
888:
887:
871:
868:
867:
864:
837:
834:
833:
805:
802:
801:
776:
773:
772:
750:
747:
746:
721:
718:
717:
695:
692:
691:
675:
672:
671:
655:
652:
651:
625:
622:
621:
605:
602:
601:
581:
579:
576:
575:
559:
557:
554:
553:
537:
535:
532:
531:
511:
509:
506:
505:
485:
483:
480:
479:
463:
461:
458:
457:
441:
439:
436:
435:
415:
413:
410:
409:
393:
391:
388:
387:
367:
365:
362:
361:
345:
343:
340:
339:
314:autocorrelation
306:neurophysiology
236:
233:
232:
210:
207:
206:
202:
198:
194:
191:autocorrelation
175:
146:
145:
121:
111:
110:
86:
76:
75:
51:
17:
12:
11:
5:
12227:
12217:
12216:
12211:
12206:
12201:
12184:
12183:
12181:
12180:
12168:
12156:
12142:
12129:
12126:
12125:
12122:
12121:
12118:
12117:
12115:
12114:
12109:
12104:
12099:
12094:
12088:
12086:
12080:
12079:
12077:
12076:
12071:
12066:
12061:
12056:
12051:
12046:
12041:
12036:
12031:
12025:
12023:
12017:
12016:
12014:
12013:
12008:
12003:
11994:
11989:
11984:
11978:
11976:
11970:
11969:
11967:
11966:
11961:
11956:
11947:
11945:Bioinformatics
11941:
11939:
11929:
11928:
11916:
11915:
11912:
11911:
11908:
11907:
11904:
11903:
11901:
11900:
11894:
11892:
11888:
11887:
11885:
11884:
11878:
11876:
11870:
11869:
11867:
11866:
11861:
11856:
11851:
11845:
11843:
11834:
11828:
11827:
11824:
11823:
11821:
11820:
11815:
11810:
11805:
11800:
11794:
11792:
11786:
11785:
11783:
11782:
11777:
11772:
11764:
11759:
11754:
11753:
11752:
11750:partial (PACF)
11741:
11739:
11733:
11732:
11730:
11729:
11724:
11719:
11711:
11706:
11700:
11698:
11697:Specific tests
11694:
11693:
11691:
11690:
11685:
11680:
11675:
11670:
11665:
11660:
11655:
11649:
11647:
11640:
11634:
11633:
11631:
11630:
11629:
11628:
11627:
11626:
11611:
11610:
11609:
11599:
11597:Classification
11594:
11589:
11584:
11579:
11574:
11569:
11563:
11561:
11555:
11554:
11552:
11551:
11546:
11544:McNemar's test
11541:
11536:
11531:
11526:
11520:
11518:
11508:
11507:
11483:
11482:
11479:
11478:
11475:
11474:
11472:
11471:
11466:
11461:
11456:
11450:
11448:
11442:
11441:
11439:
11438:
11422:
11416:
11414:
11408:
11407:
11405:
11404:
11399:
11394:
11389:
11384:
11382:Semiparametric
11379:
11374:
11368:
11366:
11362:
11361:
11359:
11358:
11353:
11348:
11343:
11337:
11335:
11329:
11328:
11326:
11325:
11320:
11315:
11310:
11305:
11299:
11297:
11291:
11290:
11288:
11287:
11282:
11277:
11272:
11266:
11264:
11254:
11253:
11250:
11249:
11244:
11238:
11230:
11229:
11226:
11225:
11222:
11221:
11219:
11218:
11217:
11216:
11206:
11201:
11196:
11195:
11194:
11189:
11178:
11176:
11170:
11169:
11166:
11165:
11163:
11162:
11157:
11156:
11155:
11147:
11139:
11123:
11120:(MannâWhitney)
11115:
11114:
11113:
11100:
11099:
11098:
11087:
11085:
11079:
11078:
11076:
11075:
11074:
11073:
11068:
11063:
11053:
11048:
11045:(ShapiroâWilk)
11040:
11035:
11030:
11025:
11020:
11012:
11006:
11004:
10998:
10997:
10995:
10994:
10986:
10977:
10965:
10959:
10957:Specific tests
10953:
10952:
10949:
10948:
10946:
10945:
10940:
10935:
10929:
10927:
10921:
10920:
10918:
10917:
10912:
10911:
10910:
10900:
10899:
10898:
10888:
10882:
10880:
10874:
10873:
10871:
10870:
10869:
10868:
10863:
10853:
10848:
10843:
10838:
10833:
10827:
10825:
10819:
10818:
10816:
10815:
10810:
10809:
10808:
10803:
10802:
10801:
10796:
10781:
10780:
10779:
10774:
10769:
10764:
10753:
10751:
10742:
10736:
10735:
10733:
10732:
10727:
10722:
10721:
10720:
10710:
10705:
10704:
10703:
10693:
10692:
10691:
10686:
10681:
10671:
10666:
10661:
10660:
10659:
10654:
10649:
10633:
10632:
10631:
10626:
10621:
10611:
10610:
10609:
10604:
10594:
10593:
10592:
10582:
10581:
10580:
10570:
10565:
10560:
10554:
10552:
10542:
10541:
10529:
10528:
10525:
10524:
10521:
10520:
10518:
10517:
10512:
10507:
10502:
10496:
10494:
10488:
10487:
10485:
10484:
10479:
10474:
10468:
10466:
10462:
10461:
10459:
10458:
10453:
10448:
10443:
10438:
10433:
10428:
10422:
10420:
10414:
10413:
10411:
10410:
10408:Standard error
10405:
10400:
10395:
10394:
10393:
10388:
10377:
10375:
10369:
10368:
10366:
10365:
10360:
10355:
10350:
10345:
10340:
10338:Optimal design
10335:
10330:
10324:
10322:
10312:
10311:
10299:
10298:
10295:
10294:
10291:
10290:
10288:
10287:
10282:
10277:
10272:
10267:
10262:
10257:
10252:
10247:
10242:
10237:
10232:
10227:
10222:
10217:
10211:
10209:
10203:
10202:
10200:
10199:
10194:
10193:
10192:
10187:
10177:
10172:
10166:
10164:
10158:
10157:
10155:
10154:
10149:
10144:
10138:
10136:
10135:Summary tables
10132:
10131:
10129:
10128:
10122:
10120:
10114:
10113:
10110:
10109:
10107:
10106:
10105:
10104:
10099:
10094:
10084:
10078:
10076:
10070:
10069:
10067:
10066:
10061:
10056:
10051:
10046:
10041:
10036:
10030:
10028:
10022:
10021:
10019:
10018:
10013:
10008:
10007:
10006:
10001:
9996:
9991:
9986:
9981:
9976:
9971:
9969:Contraharmonic
9966:
9961:
9950:
9948:
9939:
9929:
9928:
9916:
9915:
9913:
9912:
9907:
9901:
9898:
9897:
9890:
9889:
9882:
9875:
9867:
9861:
9860:
9855:
9850:
9843:
9842:External links
9840:
9839:
9838:
9812:(3): 779â797.
9799:
9796:
9794:
9793:
9786:
9768:
9751:
9744:
9718:
9709:
9702:
9679:
9664:
9638:
9631:
9613:
9572:
9533:
9526:
9500:
9493:
9467:
9455:
9446:
9436:
9434:
9431:
9429:
9428:
9423:
9418:
9413:
9408:
9403:
9401:Cross-spectrum
9398:
9393:
9388:
9383:
9378:
9373:
9368:
9366:Autocovariance
9363:
9357:
9355:
9352:
9346:
9343:
9331:
9328:
9325:
9322:
9319:
9316:
9313:
9310:
9307:
9304:
9301:
9298:
9290:
9286:
9280:
9276:
9271:
9264:
9261:
9258:
9254:
9248:
9245:
9231:
9228:
9204:
9184:
9164:
9144:
9124:
9104:
9084:
9061:
9058:
9055:
9052:
9049:
9046:
9035:CauchyâSchwarz
9015:
9012:
9009:
8985:
8982:
8979:
8976:
8973:
8952:
8945:
8942:
8939:
8935:
8930:
8924:
8921:
8918:
8914:
8908:
8885:
8881:
8877:
8874:
8871:
8868:
8865:
8862:
8859:
8856:
8853:
8850:
8847:
8844:
8841:
8838:
8816:
8812:
8808:
8805:
8802:
8799:
8796:
8793:
8790:
8787:
8784:
8781:
8778:
8775:
8772:
8769:
8738:
8712:
8708:
8687:
8665:
8661:
8640:
8637:
8634:
8631:
8628:
8625:
8605:
8602:
8599:
8596:
8593:
8590:
8570:
8546:
8540:
8536:
8532:
8529:
8526:
8523:
8520:
8517:
8514:
8510:
8505:
8499:
8495:
8491:
8488:
8485:
8482:
8479:
8476:
8473:
8469:
8460:
8456:
8450:
8446:
8441:
8434:
8431:
8428:
8424:
8418:
8415:
8390:
8387:
8384:
8381:
8378:
8375:
8355:
8352:
8349:
8346:
8343:
8340:
8319:
8316:
8303:
8300:
8297:
8294:
8291:
8288:
8285:
8282:
8279:
8276:
8269:
8265:
8262:
8257:
8254:
8251:
8247:
8244:
8241:
8235:
8229:
8226:
8223:
8220:
8217:
8212:
8183:
8180:
8166:
8162:
8159:
8156:
8153:
8150:
8145:
8142:
8138:
8131:
8128:
8125:
8122:
8119:
8114:
8111:
8107:
8084:
8080:
8075:
8071:
8067:
8062:
8058:
8054:
8051:
8046:
8043:
8039:
8032:
8029:
8024:
8020:
8016:
8011:
8007:
8003:
8000:
7995:
7992:
7988:
7975:
7972:
7970:
7967:
7945:
7941:
7935:
7931:
7924:
7918:
7914:
7908:
7904:
7900:
7895:
7892:
7889:
7885:
7880:
7873:
7867:
7863:
7859:
7854:
7850:
7845:
7840:
7836:
7833:
7827:
7819:
7815:
7809:
7805:
7799:
7796:
7793:
7790:
7785:
7782:
7778:
7771:
7768:
7765:
7762:
7757:
7754:
7750:
7722:
7719:
7716:
7713:
7710:
7707:
7685:
7682:
7678:
7654:
7649:
7645:
7641:
7636:
7632:
7628:
7623:
7619:
7615:
7610:
7606:
7599:
7593:
7589:
7581:
7577:
7572:
7568:
7561:
7557:
7552:
7547:
7540:
7532:
7528:
7523:
7519:
7512:
7508:
7503:
7498:
7493:
7489:
7486:
7480:
7474:
7469:
7465:
7461:
7456:
7452:
7448:
7443:
7439:
7435:
7430:
7426:
7420:
7415:
7411:
7407:
7402:
7398:
7394:
7391:
7386:
7383:
7379:
7372:
7369:
7364:
7360:
7356:
7351:
7347:
7343:
7338:
7335:
7331:
7307:
7304:
7272:
7267:
7263:
7259:
7254:
7250:
7246:
7226:
7215:expected value
7213:indicates the
7202:
7196:
7193:
7190:
7170:
7165:
7161:
7157:
7137:
7132:
7128:
7124:
7102:
7098:
7075:
7071:
7049:
7043:
7039:
7033:
7029:
7025:
7020:
7016:
7011:
7004:
6998:
6994:
6990:
6985:
6982:
6979:
6975:
6970:
6965:
6961:
6958:
6955:
6952:
6949:
6946:
6943:
6938:
6935:
6931:
6909:
6903:
6899:
6893:
6889:
6885:
6880:
6877:
6874:
6870:
6865:
6858:
6852:
6848:
6844:
6839:
6835:
6830:
6825:
6821:
6818:
6812:
6809:
6806:
6803:
6800:
6795:
6792:
6788:
6776:
6773:
6760:
6754:
6749:
6745:
6737:
6734:
6731:
6727:
6722:
6718:
6715:
6712:
6709:
6706:
6703:
6700:
6695:
6692:
6688:
6666:
6660:
6655:
6652:
6649:
6645:
6637:
6633:
6628:
6624:
6621:
6615:
6612:
6609:
6606:
6603:
6598:
6595:
6591:
6579:
6576:
6551:
6546:
6542:
6538:
6533:
6529:
6525:
6513:
6510:
6496:
6490:
6486:
6483:
6478:
6474:
6470:
6465:
6461:
6457:
6450:
6446:
6441:
6437:
6430:
6426:
6421:
6417:
6413:
6408:
6404:
6400:
6393:
6389:
6384:
6379:
6374:
6370:
6367:
6361:
6358:
6353:
6349:
6345:
6340:
6336:
6332:
6329:
6324:
6321:
6317:
6294:
6290:
6267:
6263:
6250:
6247:
6243:expected value
6230:
6209:
6203:
6196:
6192:
6187:
6177:
6173:
6168:
6163:
6159:
6156:
6150:
6147:
6142:
6138:
6134:
6129:
6125:
6121:
6118:
6113:
6110:
6106:
6083:
6079:
6056:
6052:
6031:
6011:
5991:
5988:
5985:
5980:
5975:
5971:
5950:
5947:
5944:
5939:
5934:
5930:
5920:and variances
5909:
5906:
5903:
5898:
5894:
5873:
5870:
5867:
5862:
5858:
5845:
5842:
5829:
5803:
5799:
5762:
5742:
5722:
5717:
5713:
5709:
5704:
5700:
5696:
5685:random process
5672:
5669:
5649:
5624:
5618:
5612:
5606:
5602:
5599:
5596:
5590:
5584:
5579:
5574:
5552:
5530:
5505:
5500:
5496:
5492:
5489:
5486:
5481:
5477:
5473:
5470:
5466:
5445:
5440:
5436:
5432:
5429:
5426:
5421:
5417:
5413:
5410:
5406:
5393:
5390:
5377:
5372:
5368:
5362:
5358:
5354:
5351:
5348:
5328:
5325:
5322:
5319:
5316:
5296:
5293:
5290:
5267:
5262:
5257:
5235:
5229:
5225:
5221:
5216:
5212:
5207:
5203:
5199:
5177:
5171:
5167:
5163:
5158:
5154:
5150:
5145:
5141:
5136:
5132:
5128:
5115:
5112:
5095:
5074:
5052:
5029:
5023:
5018:
5014:
5008:
5004:
5000:
4997:
4994:
4991:
4989:
4986:
4984:
4979:
4975:
4969:
4965:
4961:
4958:
4955:
4952:
4950:
4945:
4941:
4935:
4931:
4927:
4924:
4921:
4918:
4917:
4914:
4911:
4908:
4906:
4903:
4901:
4898:
4896:
4893:
4892:
4889:
4886:
4881:
4877:
4871:
4867:
4863:
4860:
4857:
4854:
4852:
4849:
4847:
4842:
4838:
4832:
4828:
4824:
4821:
4818:
4815:
4813:
4808:
4804:
4798:
4794:
4790:
4787:
4784:
4781:
4780:
4777:
4774:
4769:
4765:
4759:
4755:
4751:
4748:
4745:
4742:
4740:
4737:
4735:
4730:
4726:
4720:
4716:
4712:
4709:
4706:
4703:
4701:
4696:
4692:
4686:
4682:
4678:
4675:
4672:
4669:
4668:
4666:
4661:
4655:
4650:
4645:
4624:
4621:
4618:
4597:
4592:
4587:
4582:
4578:
4575:
4569:
4563:
4558:
4553:
4531:
4509:
4489:expected value
4472:
4467:
4463:
4459:
4456:
4453:
4448:
4444:
4440:
4437:
4433:
4412:
4407:
4403:
4399:
4396:
4393:
4388:
4384:
4380:
4377:
4373:
4362:random vectors
4357:
4354:
4349:Main article:
4346:
4343:
4341:
4340:
4339:
4338:
4326:
4323:
4319:
4315:
4312:
4309:
4305:
4301:
4297:
4293:
4290:
4287:
4283:
4279:
4276:
4254:
4234:
4214:
4194:
4174:
4154:
4143:
4132:
4110:
4105:
4101:
4098:
4095:
4092:
4088:
4082:
4074:
4070:
4065:
4061:
4058:
4055:
4052:
4049:
4043:
4037:
4015:
3993:
3990:
3962:
3950:
3939:
3935:
3932:
3929:
3923:
3918:
3913:
3908:
3905:
3902:
3896:
3888:
3884:
3880:
3877:
3874:
3870:
3864:
3846:
3833:
3829:
3826:
3823:
3819:
3815:
3811:
3807:
3804:
3801:
3797:
3793:
3789:
3785:
3782:
3779:
3775:
3771:
3767:
3763:
3760:
3757:
3753:
3742:
3730:
3727:
3724:
3721:
3718:
3715:
3712:
3692:
3672:
3661:
3650:
3647:
3644:
3641:
3638:
3635:
3632:
3629:
3605:
3594:
3583:
3580:
3577:
3574:
3571:
3568:
3563:
3559:
3556:
3553:
3550:
3544:
3539:
3535:
3532:
3529:
3526:
3520:
3517:
3514:
3511:
3508:
3505:
3502:
3499:
3496:
3493:
3490:
3487:
3484:
3481:
3478:
3475:
3465:
3464:
3463:
3452:
3449:
3446:
3443:
3440:
3437:
3434:
3431:
3428:
3425:
3420:
3416:
3413:
3410:
3407:
3404:
3398:
3395:
3392:
3389:
3386:
3383:
3380:
3377:
3374:
3371:
3368:
3365:
3362:
3359:
3356:
3353:
3331:
3328:
3325:
3322:
3300:
3296:
3293:
3290:
3287:
3284:
3261:
3237:
3234:
3231:
3228:
3208:
3205:
3202:
3199:
3187:
3185:
3182:
3162:
3138:
3118:
3078:
3075:
3072:
3069:
3066:
3046:
3026:
3006:
2986:
2966:
2954:
2951:
2937:
2934:
2931:
2926:
2922:
2912:Specifically,
2892:
2887:
2882:
2877:
2872:
2867:
2864:
2861:
2858:
2853:
2849:
2827:
2823:
2818:
2813:
2808:
2803:
2798:
2793:
2790:
2787:
2784:
2781:
2778:
2775:
2755:
2752:
2749:
2746:
2743:
2738:
2735:
2732:
2728:
2724:
2721:
2718:
2715:
2712:
2709:
2706:
2703:
2700:
2697:
2694:
2689:
2685:
2681:
2678:
2675:
2672:
2669:
2666:
2663:
2660:
2657:
2652:
2648:
2644:
2641:
2638:
2635:
2632:
2629:
2624:
2620:
2599:
2594:
2582:
2578:
2575:
2572:
2569:
2566:
2561:
2557:
2551:
2547:
2544:
2541:
2538:
2530:
2527:
2524:
2519:
2516:
2513:
2509:
2505:
2499:
2496:
2493:
2490:
2487:
2484:
2481:
2478:
2456:
2451:
2446:
2443:
2421:
2416:
2411:
2408:
2388:
2385:
2382:
2379:
2374:
2370:
2365:
2353:
2349:
2346:
2343:
2340:
2337:
2334:
2326:
2323:
2320:
2315:
2312:
2309:
2305:
2301:
2295:
2292:
2289:
2286:
2283:
2280:
2277:
2274:
2254:
2249:
2237:
2233:
2230:
2227:
2224:
2221:
2218:
2213:
2209:
2206:
2203:
2200:
2192:
2189:
2186:
2181:
2178:
2175:
2171:
2167:
2161:
2158:
2155:
2152:
2149:
2146:
2143:
2140:
2118:
2113:
2108:
2105:
2102:
2099:
2079:
2076:
2073:
2070:
2065:
2061:
2058:
2055:
2052:
2049:
2046:
2038:
2033:
2030:
2027:
2024:
2020:
2016:
2010:
2007:
2004:
2001:
1998:
1995:
1992:
1989:
1969:
1966:
1963:
1960:
1957:
1954:
1949:
1945:
1942:
1939:
1936:
1928:
1923:
1920:
1917:
1914:
1910:
1906:
1900:
1897:
1894:
1891:
1888:
1885:
1882:
1879:
1859:
1856:
1852:
1849:
1846:
1843:
1838:
1834:
1831:
1828:
1825:
1822:
1819:
1811:
1808:
1803:
1799:
1791:
1787:
1782:
1778:
1772:
1769:
1766:
1763:
1760:
1757:
1754:
1751:
1731:
1728:
1724:
1721:
1718:
1715:
1712:
1709:
1704:
1700:
1697:
1694:
1691:
1683:
1680:
1675:
1671:
1663:
1659:
1654:
1650:
1644:
1641:
1638:
1635:
1632:
1629:
1626:
1623:
1603:
1583:
1580:
1577:
1572:
1568:
1564:
1559:
1555:
1551:
1531:
1511:
1508:
1488:
1468:
1448:
1425:
1405:
1382:
1362:
1359:
1356:
1336:
1316:
1296:
1276:
1256:
1236:
1208:
1188:
1185:
1182:
1179:
1153:
1149:
1146:
1143:
1140:
1117:
1114:
1110:
1107:
1104:
1101:
1096:
1092:
1089:
1086:
1083:
1080:
1077:
1069:
1064:
1061:
1057:
1053:
1047:
1044:
1041:
1038:
1035:
1032:
1029:
1026:
1006:
1003:
999:
996:
993:
990:
987:
984:
979:
975:
972:
969:
966:
958:
953:
950:
946:
942:
936:
933:
930:
927:
924:
921:
918:
915:
895:
875:
863:
860:
847:
844:
841:
821:
818:
815:
812:
809:
789:
786:
783:
780:
760:
757:
754:
731:
728:
725:
705:
702:
699:
679:
659:
629:
609:
584:
562:
540:
514:
488:
466:
444:
418:
396:
370:
348:
337:random vectors
331:refers to the
246:
243:
240:
220:
217:
214:
205:is the reason
177:
176:
174:
173:
166:
159:
151:
148:
147:
144:
143:
138:
133:
128:
122:
117:
116:
113:
112:
109:
108:
103:
98:
93:
87:
82:
81:
78:
77:
74:
73:
68:
63:
58:
52:
47:
46:
43:
42:
34:
33:
27:
26:
15:
9:
6:
4:
3:
2:
12226:
12215:
12212:
12210:
12207:
12205:
12202:
12200:
12199:Bilinear maps
12197:
12196:
12194:
12179:
12178:
12169:
12167:
12166:
12157:
12155:
12154:
12149:
12143:
12141:
12140:
12131:
12130:
12127:
12113:
12110:
12108:
12107:Geostatistics
12105:
12103:
12100:
12098:
12095:
12093:
12090:
12089:
12087:
12085:
12081:
12075:
12074:Psychometrics
12072:
12070:
12067:
12065:
12062:
12060:
12057:
12055:
12052:
12050:
12047:
12045:
12042:
12040:
12037:
12035:
12032:
12030:
12027:
12026:
12024:
12022:
12018:
12012:
12009:
12007:
12004:
12002:
11998:
11995:
11993:
11990:
11988:
11985:
11983:
11980:
11979:
11977:
11975:
11971:
11965:
11962:
11960:
11957:
11955:
11951:
11948:
11946:
11943:
11942:
11940:
11938:
11937:Biostatistics
11934:
11930:
11926:
11921:
11917:
11899:
11898:Log-rank test
11896:
11895:
11893:
11889:
11883:
11880:
11879:
11877:
11875:
11871:
11865:
11862:
11860:
11857:
11855:
11852:
11850:
11847:
11846:
11844:
11842:
11838:
11835:
11833:
11829:
11819:
11816:
11814:
11811:
11809:
11806:
11804:
11801:
11799:
11796:
11795:
11793:
11791:
11787:
11781:
11778:
11776:
11773:
11771:
11769:(BoxâJenkins)
11765:
11763:
11760:
11758:
11755:
11751:
11748:
11747:
11746:
11743:
11742:
11740:
11738:
11734:
11728:
11725:
11723:
11722:DurbinâWatson
11720:
11718:
11712:
11710:
11707:
11705:
11704:DickeyâFuller
11702:
11701:
11699:
11695:
11689:
11686:
11684:
11681:
11679:
11678:Cointegration
11676:
11674:
11671:
11669:
11666:
11664:
11661:
11659:
11656:
11654:
11653:Decomposition
11651:
11650:
11648:
11644:
11641:
11639:
11635:
11625:
11622:
11621:
11620:
11617:
11616:
11615:
11612:
11608:
11605:
11604:
11603:
11600:
11598:
11595:
11593:
11590:
11588:
11585:
11583:
11580:
11578:
11575:
11573:
11570:
11568:
11565:
11564:
11562:
11560:
11556:
11550:
11547:
11545:
11542:
11540:
11537:
11535:
11532:
11530:
11527:
11525:
11524:Cohen's kappa
11522:
11521:
11519:
11517:
11513:
11509:
11505:
11501:
11497:
11493:
11488:
11484:
11470:
11467:
11465:
11462:
11460:
11457:
11455:
11452:
11451:
11449:
11447:
11443:
11437:
11433:
11429:
11423:
11421:
11418:
11417:
11415:
11413:
11409:
11403:
11400:
11398:
11395:
11393:
11390:
11388:
11385:
11383:
11380:
11378:
11377:Nonparametric
11375:
11373:
11370:
11369:
11367:
11363:
11357:
11354:
11352:
11349:
11347:
11344:
11342:
11339:
11338:
11336:
11334:
11330:
11324:
11321:
11319:
11316:
11314:
11311:
11309:
11306:
11304:
11301:
11300:
11298:
11296:
11292:
11286:
11283:
11281:
11278:
11276:
11273:
11271:
11268:
11267:
11265:
11263:
11259:
11255:
11248:
11245:
11243:
11240:
11239:
11235:
11231:
11215:
11212:
11211:
11210:
11207:
11205:
11202:
11200:
11197:
11193:
11190:
11188:
11185:
11184:
11183:
11180:
11179:
11177:
11175:
11171:
11161:
11158:
11154:
11148:
11146:
11140:
11138:
11132:
11131:
11130:
11127:
11126:Nonparametric
11124:
11122:
11116:
11112:
11109:
11108:
11107:
11101:
11097:
11096:Sample median
11094:
11093:
11092:
11089:
11088:
11086:
11084:
11080:
11072:
11069:
11067:
11064:
11062:
11059:
11058:
11057:
11054:
11052:
11049:
11047:
11041:
11039:
11036:
11034:
11031:
11029:
11026:
11024:
11021:
11019:
11017:
11013:
11011:
11008:
11007:
11005:
11003:
10999:
10993:
10991:
10987:
10985:
10983:
10978:
10976:
10971:
10967:
10966:
10963:
10960:
10958:
10954:
10944:
10941:
10939:
10936:
10934:
10931:
10930:
10928:
10926:
10922:
10916:
10913:
10909:
10906:
10905:
10904:
10901:
10897:
10894:
10893:
10892:
10889:
10887:
10884:
10883:
10881:
10879:
10875:
10867:
10864:
10862:
10859:
10858:
10857:
10854:
10852:
10849:
10847:
10844:
10842:
10839:
10837:
10834:
10832:
10829:
10828:
10826:
10824:
10820:
10814:
10811:
10807:
10804:
10800:
10797:
10795:
10792:
10791:
10790:
10787:
10786:
10785:
10782:
10778:
10775:
10773:
10770:
10768:
10765:
10763:
10760:
10759:
10758:
10755:
10754:
10752:
10750:
10746:
10743:
10741:
10737:
10731:
10728:
10726:
10723:
10719:
10716:
10715:
10714:
10711:
10709:
10706:
10702:
10701:loss function
10699:
10698:
10697:
10694:
10690:
10687:
10685:
10682:
10680:
10677:
10676:
10675:
10672:
10670:
10667:
10665:
10662:
10658:
10655:
10653:
10650:
10648:
10642:
10639:
10638:
10637:
10634:
10630:
10627:
10625:
10622:
10620:
10617:
10616:
10615:
10612:
10608:
10605:
10603:
10600:
10599:
10598:
10595:
10591:
10588:
10587:
10586:
10583:
10579:
10576:
10575:
10574:
10571:
10569:
10566:
10564:
10561:
10559:
10556:
10555:
10553:
10551:
10547:
10543:
10539:
10534:
10530:
10516:
10513:
10511:
10508:
10506:
10503:
10501:
10498:
10497:
10495:
10493:
10489:
10483:
10480:
10478:
10475:
10473:
10470:
10469:
10467:
10463:
10457:
10454:
10452:
10449:
10447:
10444:
10442:
10439:
10437:
10434:
10432:
10429:
10427:
10424:
10423:
10421:
10419:
10415:
10409:
10406:
10404:
10403:Questionnaire
10401:
10399:
10396:
10392:
10389:
10387:
10384:
10383:
10382:
10379:
10378:
10376:
10374:
10370:
10364:
10361:
10359:
10356:
10354:
10351:
10349:
10346:
10344:
10341:
10339:
10336:
10334:
10331:
10329:
10326:
10325:
10323:
10321:
10317:
10313:
10309:
10304:
10300:
10286:
10283:
10281:
10278:
10276:
10273:
10271:
10268:
10266:
10263:
10261:
10258:
10256:
10253:
10251:
10248:
10246:
10243:
10241:
10238:
10236:
10233:
10231:
10230:Control chart
10228:
10226:
10223:
10221:
10218:
10216:
10213:
10212:
10210:
10208:
10204:
10198:
10195:
10191:
10188:
10186:
10183:
10182:
10181:
10178:
10176:
10173:
10171:
10168:
10167:
10165:
10163:
10159:
10153:
10150:
10148:
10145:
10143:
10140:
10139:
10137:
10133:
10127:
10124:
10123:
10121:
10119:
10115:
10103:
10100:
10098:
10095:
10093:
10090:
10089:
10088:
10085:
10083:
10080:
10079:
10077:
10075:
10071:
10065:
10062:
10060:
10057:
10055:
10052:
10050:
10047:
10045:
10042:
10040:
10037:
10035:
10032:
10031:
10029:
10027:
10023:
10017:
10014:
10012:
10009:
10005:
10002:
10000:
9997:
9995:
9992:
9990:
9987:
9985:
9982:
9980:
9977:
9975:
9972:
9970:
9967:
9965:
9962:
9960:
9957:
9956:
9955:
9952:
9951:
9949:
9947:
9943:
9940:
9938:
9934:
9930:
9926:
9921:
9917:
9911:
9908:
9906:
9903:
9902:
9899:
9895:
9888:
9883:
9881:
9876:
9874:
9869:
9868:
9865:
9859:
9856:
9854:
9851:
9849:
9846:
9845:
9835:
9831:
9827:
9823:
9819:
9815:
9811:
9807:
9802:
9801:
9789:
9783:
9779:
9772:
9764:
9763:
9755:
9747:
9741:
9737:
9733:
9729:
9722:
9713:
9705:
9699:
9695:
9688:
9686:
9684:
9675:
9671:
9667:
9661:
9657:
9653:
9649:
9642:
9634:
9628:
9624:
9617:
9609:
9605:
9600:
9595:
9591:
9587:
9583:
9576:
9567:
9562:
9557:
9552:
9548:
9544:
9537:
9529:
9523:
9519:
9514:
9513:
9504:
9496:
9490:
9486:
9481:
9480:
9471:
9465:
9459:
9450:
9441:
9437:
9427:
9424:
9422:
9419:
9417:
9414:
9412:
9409:
9407:
9404:
9402:
9399:
9397:
9394:
9392:
9389:
9387:
9384:
9382:
9379:
9377:
9374:
9372:
9369:
9367:
9364:
9362:
9359:
9358:
9351:
9342:
9326:
9323:
9320:
9314:
9308:
9305:
9302:
9296:
9288:
9284:
9278:
9274:
9269:
9262:
9259:
9256:
9252:
9246:
9243:
9227:
9225:
9221:
9216:
9202:
9182:
9162:
9155:, being thus
9142:
9122:
9102:
9082:
9073:
9056:
9053:
9050:
9047:
9036:
9032:
9030:
9010:
8999:
8998:inner product
8980:
8977:
8974:
8950:
8940:
8933:
8928:
8919:
8912:
8906:
8883:
8879:
8875:
8869:
8866:
8863:
8857:
8854:
8848:
8845:
8842:
8836:
8814:
8810:
8806:
8800:
8797:
8794:
8788:
8785:
8779:
8776:
8773:
8767:
8760:. That is, if
8759:
8755:
8750:
8736:
8728:
8710:
8706:
8685:
8663:
8659:
8635:
8632:
8629:
8623:
8600:
8597:
8594:
8588:
8568:
8558:
8544:
8538:
8534:
8530:
8524:
8521:
8518:
8512:
8508:
8503:
8497:
8493:
8489:
8483:
8480:
8477:
8471:
8467:
8458:
8454:
8448:
8444:
8439:
8432:
8429:
8426:
8422:
8416:
8413:
8402:
8385:
8382:
8379:
8373:
8350:
8347:
8344:
8338:
8330:
8325:
8315:
8295:
8286:
8283:
8280:
8263:
8260:
8233:
8210:
8201:
8197:
8192:
8188:
8179:
8157:
8154:
8148:
8143:
8140:
8129:
8123:
8117:
8112:
8109:
8073:
8069:
8065:
8060:
8056:
8049:
8044:
8041:
8030:
8022:
8018:
8014:
8009:
8005:
7998:
7993:
7990:
7966:
7964:
7943:
7939:
7933:
7929:
7922:
7912:
7906:
7902:
7898:
7893:
7890:
7887:
7883:
7878:
7871:
7865:
7861:
7857:
7852:
7848:
7843:
7838:
7834:
7825:
7817:
7813:
7807:
7803:
7794:
7788:
7783:
7780:
7769:
7763:
7755:
7752:
7748:
7738:
7736:
7717:
7714:
7711:
7708:
7683:
7680:
7676:
7647:
7643:
7634:
7630:
7621:
7617:
7608:
7604:
7597:
7587:
7579:
7575:
7570:
7566:
7559:
7555:
7550:
7545:
7538:
7530:
7526:
7521:
7517:
7510:
7506:
7501:
7496:
7491:
7487:
7478:
7467:
7463:
7454:
7450:
7441:
7437:
7428:
7424:
7413:
7409:
7405:
7400:
7396:
7389:
7384:
7381:
7370:
7362:
7358:
7354:
7349:
7345:
7336:
7333:
7329:
7319:
7317:
7313:
7306:Normalization
7303:
7301:
7296:
7293:
7288:
7286:
7265:
7261:
7257:
7252:
7248:
7224:
7216:
7191:
7163:
7159:
7130:
7126:
7100:
7096:
7073:
7069:
7047:
7037:
7031:
7027:
7023:
7018:
7014:
7009:
7002:
6996:
6992:
6988:
6983:
6980:
6977:
6973:
6968:
6963:
6959:
6953:
6947:
6941:
6936:
6933:
6907:
6897:
6891:
6887:
6883:
6878:
6875:
6872:
6868:
6863:
6856:
6850:
6846:
6842:
6837:
6833:
6828:
6823:
6819:
6810:
6804:
6798:
6793:
6790:
6772:
6758:
6747:
6743:
6735:
6732:
6729:
6725:
6720:
6716:
6710:
6704:
6698:
6693:
6690:
6664:
6653:
6650:
6647:
6643:
6635:
6631:
6626:
6622:
6613:
6607:
6601:
6596:
6593:
6575:
6573:
6569:
6565:
6544:
6540:
6536:
6531:
6527:
6509:
6494:
6476:
6472:
6463:
6459:
6455:
6448:
6444:
6439:
6428:
6419:
6415:
6406:
6402:
6398:
6391:
6387:
6382:
6377:
6372:
6368:
6359:
6351:
6347:
6343:
6338:
6334:
6327:
6322:
6319:
6292:
6288:
6265:
6261:
6246:
6244:
6207:
6194:
6190:
6185:
6175:
6171:
6166:
6161:
6157:
6148:
6140:
6136:
6132:
6127:
6123:
6116:
6111:
6108:
6081:
6077:
6054:
6050:
6029:
6009:
5986:
5978:
5973:
5969:
5945:
5937:
5932:
5928:
5904:
5896:
5892:
5868:
5860:
5856:
5841:
5827:
5819:
5801:
5797:
5788:
5784:
5781:process or a
5780:
5779:discrete-time
5776:
5760:
5740:
5715:
5711:
5707:
5702:
5698:
5686:
5682:
5678:
5668:
5666:
5597:
5588:
5564:is defined by
5519:
5498:
5494:
5490:
5487:
5484:
5479:
5475:
5468:
5438:
5434:
5430:
5427:
5424:
5419:
5415:
5408:
5389:
5370:
5366:
5360:
5356:
5349:
5339:-th entry is
5323:
5320:
5317:
5307:matrix whose
5294:
5291:
5288:
5233:
5227:
5223:
5219:
5214:
5210:
5205:
5201:
5175:
5169:
5165:
5161:
5156:
5152:
5148:
5143:
5139:
5134:
5130:
5111:
5109:
5027:
5016:
5012:
5006:
5002:
4995:
4987:
4977:
4973:
4967:
4963:
4956:
4943:
4939:
4933:
4929:
4922:
4909:
4904:
4899:
4894:
4879:
4875:
4869:
4865:
4858:
4850:
4840:
4836:
4830:
4826:
4819:
4806:
4802:
4796:
4792:
4785:
4767:
4763:
4757:
4753:
4746:
4738:
4728:
4724:
4718:
4714:
4707:
4694:
4690:
4684:
4680:
4673:
4664:
4659:
4622:
4619:
4616:
4595:
4580:
4576:
4567:
4543:is defined by
4498:
4494:
4490:
4486:
4465:
4461:
4457:
4454:
4451:
4446:
4442:
4435:
4405:
4401:
4397:
4394:
4391:
4386:
4382:
4375:
4363:
4352:
4324:
4321:
4317:
4313:
4310:
4307:
4303:
4299:
4295:
4291:
4288:
4285:
4281:
4277:
4274:
4267:
4266:
4252:
4232:
4212:
4192:
4172:
4152:
4144:
4141:
4137:
4133:
4130:
4126:
4103:
4096:
4090:
4086:
4072:
4068:
4056:
4053:
4047:
4041:
4013:
3988:
3978:
3937:
3933:
3930:
3927:
3916:
3906:
3903:
3900:
3886:
3882:
3878:
3875:
3872:
3868:
3853:
3851:
3847:
3831:
3827:
3824:
3821:
3817:
3813:
3809:
3805:
3802:
3799:
3795:
3791:
3787:
3783:
3780:
3777:
3773:
3769:
3765:
3761:
3758:
3755:
3751:
3743:
3728:
3725:
3722:
3719:
3716:
3713:
3710:
3690:
3670:
3662:
3648:
3645:
3642:
3639:
3636:
3633:
3630:
3627:
3619:
3603:
3595:
3581:
3575:
3572:
3554:
3548:
3542:
3530:
3524:
3515:
3509:
3497:
3491:
3488:
3482:
3476:
3466:
3450:
3444:
3432:
3426:
3423:
3411:
3408:
3402:
3393:
3387:
3375:
3369:
3366:
3360:
3354:
3344:
3343:
3326:
3320:
3291:
3288:
3282:
3259:
3251:
3232:
3226:
3203:
3197:
3189:
3188:
3181:
3179:
3174:
3160:
3152:
3149:, taking the
3136:
3116:
3109:
3101:
3095:
3091:
3073:
3070:
3067:
3044:
3024:
3004:
2984:
2964:
2950:
2932:
2924:
2920:
2910:
2908:
2890:
2875:
2865:
2859:
2851:
2847:
2816:
2806:
2801:
2791:
2785:
2782:
2779:
2773:
2744:
2736:
2733:
2730:
2726:
2722:
2719:
2713:
2710:
2707:
2704:
2695:
2687:
2683:
2679:
2676:
2670:
2667:
2658:
2650:
2646:
2642:
2639:
2633:
2627:
2622:
2618:
2592:
2576:
2573:
2570:
2559:
2555:
2542:
2536:
2528:
2525:
2522:
2517:
2514:
2511:
2507:
2503:
2494:
2485:
2482:
2479:
2454:
2444:
2441:
2419:
2409:
2406:
2383:
2377:
2363:
2347:
2344:
2341:
2332:
2324:
2321:
2318:
2313:
2310:
2307:
2303:
2299:
2290:
2281:
2278:
2275:
2247:
2231:
2228:
2225:
2216:
2204:
2198:
2190:
2187:
2184:
2179:
2176:
2173:
2169:
2165:
2156:
2147:
2144:
2141:
2116:
2106:
2103:
2100:
2097:
2074:
2068:
2056:
2053:
2050:
2044:
2028:
2025:
2022:
2018:
2014:
2005:
1996:
1993:
1990:
1964:
1961:
1958:
1952:
1940:
1934:
1918:
1915:
1912:
1908:
1904:
1895:
1886:
1883:
1880:
1857:
1854:
1847:
1841:
1829:
1826:
1823:
1817:
1809:
1806:
1801:
1797:
1789:
1785:
1780:
1776:
1767:
1758:
1755:
1752:
1729:
1726:
1719:
1716:
1713:
1707:
1695:
1689:
1681:
1678:
1673:
1669:
1661:
1657:
1652:
1648:
1639:
1630:
1627:
1624:
1601:
1578:
1575:
1570:
1566:
1562:
1557:
1553:
1506:
1486:
1466:
1446:
1437:
1423:
1403:
1396:
1380:
1360:
1357:
1354:
1334:
1314:
1294:
1274:
1254:
1234:
1226:
1222:
1206:
1183:
1177:
1169:
1144:
1138:
1115:
1112:
1105:
1099:
1087:
1084:
1081:
1075:
1059:
1055:
1051:
1042:
1033:
1030:
1027:
1004:
1001:
994:
991:
988:
982:
970:
964:
948:
944:
940:
931:
922:
919:
916:
893:
873:
859:
845:
842:
839:
816:
813:
807:
784:
778:
758:
755:
752:
745:
729:
726:
723:
703:
700:
697:
677:
657:
650:
646:
643:
627:
607:
598:
529:
526:are known as
503:
456:. If each of
433:
385:
338:
334:
330:
326:
322:
317:
315:
311:
307:
303:
302:cryptanalysis
299:
295:
291:
287:
283:
279:
278:
272:
268:
264:
244:
241:
238:
218:
215:
212:
192:
188:
183:
172:
167:
165:
160:
158:
153:
152:
150:
149:
142:
139:
137:
134:
132:
129:
127:
124:
123:
120:
115:
114:
107:
104:
102:
99:
97:
94:
92:
89:
88:
85:
80:
79:
72:
69:
67:
64:
62:
59:
57:
54:
53:
50:
45:
44:
40:
36:
35:
32:
29:
28:
25:
21:
20:
12175:
12163:
12144:
12137:
12049:Econometrics
11999: /
11982:Chemometrics
11959:Epidemiology
11952: /
11925:Applications
11767:ARIMA model
11756:
11714:Q-statistic
11663:Stationarity
11559:Multivariate
11502: /
11498: /
11496:Multivariate
11494: /
11434: /
11430: /
11204:Bayes factor
11103:Signed rank
11015:
10989:
10981:
10969:
10664:Completeness
10500:Cohort study
10398:Opinion poll
10333:Missing data
10320:Study design
10275:Scatter plot
10197:Scatter plot
10190:Spearman's Ď
10152:Grouped data
9809:
9805:
9777:
9771:
9761:
9754:
9727:
9721:
9712:
9693:
9647:
9641:
9622:
9616:
9589:
9585:
9575:
9566:10356/105527
9542:
9536:
9511:
9503:
9478:
9470:
9458:
9449:
9440:
9348:
9233:
9217:
9074:
9028:
8751:
8559:
8403:
8321:
8199:
8190:
8186:
8185:
7977:
7739:
7320:
7309:
7300:sub-sampling
7289:
7284:
6778:
6581:
6515:
6252:
5847:
5674:
5395:
5117:
4496:
4359:
3975:denotes the
3252:(denoted by
3178:econometrics
3175:
3105:
2956:
2911:
1438:
1394:
1224:
1221:displacement
1220:
1166:denotes the
865:
599:
527:
384:correlations
383:
382:, while the
333:correlations
328:
318:
281:
274:
266:
260:
118:
83:
48:
12177:WikiProject
12092:Cartography
12054:Jurimetrics
12006:Reliability
11737:Time domain
11716:(LjungâBox)
11638:Time-series
11516:Categorical
11500:Time-series
11492:Categorical
11427:(Bernoulli)
11262:Correlation
11242:Correlation
11038:JarqueâBera
11010:Chi-squared
10772:M-estimator
10725:Asymptotics
10669:Sufficiency
10436:Interaction
10348:Replication
10328:Effect size
10285:Violin plot
10265:Radar chart
10245:Forest plot
10235:Correlogram
10185:Kendall's Ď
9381:Correlation
9376:Convolution
6570:. Then the
6022:, for each
5818:realization
5783:real number
4495:exist, the
3342:. That is:
3250:convolution
2953:Explanation
744:convolution
642:independent
502:time series
327:, the term
321:probability
310:convolution
277:dot product
187:convolution
12193:Categories
12044:Demography
11762:ARMA model
11567:Regression
11144:(Friedman)
11105:(Wilcoxon)
11043:Normality
11033:Lilliefors
10980:Student's
10856:Resampling
10730:Robustness
10718:divergence
10708:Efficiency
10646:(monotone)
10641:Likelihood
10558:Population
10391:Stratified
10343:Population
10162:Dependence
10118:Count data
10049:Percentile
10026:Dispersion
9959:Arithmetic
9894:Statistics
9632:0691043019
9527:0139141014
9494:0132136031
9433:References
7969:Properties
5773:may be an
5681:statistics
4356:Definition
3184:Properties
1594:of length
1219:is called
325:statistics
24:Statistics
11425:Logistic
11192:posterior
11118:Rank sum
10866:Jackknife
10861:Bootstrap
10679:Bootstrap
10614:Parameter
10563:Statistic
10358:Statistic
10270:Run chart
10255:Pie chart
10250:Histogram
10240:Fan chart
10215:Bar chart
10097:L-moments
9984:Geometric
9780:. Wiley.
9371:Coherence
9285:σ
9275:σ
9253:∑
9075:Thus, if
9048:−
9014:‖
9011:⋅
9008:‖
8984:⟩
8981:⋅
8975:⋅
8972:⟨
8944:‖
8938:‖
8923:‖
8917:‖
8880:μ
8876:−
8811:μ
8807:−
8707:σ
8660:μ
8535:μ
8531:−
8494:μ
8490:−
8455:σ
8445:σ
8423:∑
8284:⋆
8264:∈
8211:τ
8165:¯
8158:τ
8155:−
8149:
8124:τ
8118:
8083:¯
8050:
7999:
7940:σ
7930:σ
7917:¯
7903:μ
7899:−
7894:τ
7862:μ
7858:−
7835:
7814:σ
7804:σ
7795:τ
7789:
7764:τ
7749:ρ
7709:−
7677:ρ
7631:σ
7605:σ
7592:¯
7571:μ
7567:−
7522:μ
7518:−
7488:
7451:σ
7425:σ
7390:
7330:ρ
7192:
7097:σ
7070:μ
7042:¯
7028:μ
7024:−
6993:μ
6989:−
6984:τ
6981:−
6960:
6948:τ
6942:
6902:¯
6888:μ
6884:−
6879:τ
6847:μ
6843:−
6820:
6811:≜
6805:τ
6799:
6753:¯
6736:τ
6733:−
6717:
6705:τ
6699:
6659:¯
6654:τ
6623:
6614:≜
6608:τ
6602:
6566:that are
6489:¯
6460:μ
6456:−
6403:μ
6399:−
6369:
6360:≜
6328:
6202:¯
6158:
6149:≜
6117:
5970:σ
5929:σ
5893:μ
5857:μ
5598:
5589:≜
5488:…
5428:…
5350:
5292:×
4996:
4988:⋯
4957:
4923:
4910:⋮
4905:⋱
4900:⋮
4895:⋮
4859:
4851:⋯
4820:
4786:
4747:
4739:⋯
4708:
4674:
4620:×
4577:
4568:≜
4455:…
4395:…
4322:∗
4311:⋆
4289:∗
4278:⋆
4109:¯
4064:¯
4054:−
3992:¯
3979:, and an
3917:⋅
3912:¯
3876:⋆
3825:⋆
3814:⋆
3803:⋆
3781:⋆
3770:⋆
3759:⋆
3726:⋆
3714:⋆
3643:∗
3631:⋆
3573:−
3562:¯
3543:⋆
3538:¯
3489:⋆
3424:∗
3419:¯
3409:−
3367:⋆
3299:¯
3289:−
3260:∗
3151:conjugate
3071:⋆
2933:⋅
2881:→
2866::
2860:⋅
2822:→
2807:×
2792::
2786:⋅
2780:⋅
2734:−
2708:…
2550:¯
2526:−
2508:∑
2504:≜
2483:⋆
2445:∈
2410:∈
2373:¯
2345:−
2322:−
2304:∑
2300:≜
2279:⋆
2212:¯
2188:−
2170:∑
2166:≜
2145:⋆
2107:∈
2064:¯
2054:−
2037:∞
2032:∞
2029:−
2019:∑
2015:≜
1994:⋆
1948:¯
1927:∞
1922:∞
1919:−
1909:∑
1905:≜
1884:⋆
1837:¯
1830:τ
1827:−
1781:∫
1777:≜
1768:τ
1756:⋆
1720:τ
1703:¯
1653:∫
1649:≜
1640:τ
1628:⋆
1530:∞
1510:∞
1507:−
1424:τ
1361:τ
1275:τ
1207:τ
1152:¯
1095:¯
1088:τ
1085:−
1068:∞
1063:∞
1060:−
1056:∫
1052:≜
1043:τ
1031:⋆
995:τ
978:¯
957:∞
952:∞
949:−
945:∫
941:≜
932:τ
920:⋆
814:−
756:∗
727:⋆
701:−
298:averaging
242:⋆
216:∗
12139:Category
11832:Survival
11709:Johansen
11432:Binomial
11387:Isotonic
10974:(normal)
10619:location
10426:Blocking
10381:Sampling
10260:QâQ plot
10225:Box plot
10207:Graphics
10102:Skewness
10092:Kurtosis
10064:Variance
9994:Heronian
9989:Harmonic
9834:62710397
9674:17108908
9354:See also
8951:⟩
8907:⟨
6002:at time
5663:denotes
4493:variance
4026:, since
3663:If both
1373:, hence
640:are two
275:sliding
12165:Commons
12112:Kriging
11997:Process
11954:studies
11813:Wavelet
11646:General
10813:Plug-in
10607:L space
10386:Cluster
10087:Moments
9905:Outline
9814:Bibcode
9608:3544911
9485:147â148
9195:equals
9026:is the
8996:is the
8202:, as in
8198:of the
8196:arg max
7285:jointly
6241:is the
5775:integer
5114:Example
5106:is the
3620:, then
12034:Census
11624:Normal
11572:Manova
11392:Robust
11142:2-way
11134:1-way
10972:-test
10643:
10220:Biplot
10011:Median
10004:Lehmer
9946:Center
9832:
9784:
9742:
9700:
9672:
9662:
9629:
9606:
9524:
9491:
9031:² norm
8964:where
8561:where
7198:
7061:where
6814:
6617:
6363:
6221:where
6152:
5785:for a
5777:for a
5635:where
5592:
4571:
4487:whose
3951:where
2905:is an
2610:where
2590:
2501:
2361:
2297:
2245:
2163:
2012:
1902:
1774:
1646:
1199:, and
1128:where
1049:
938:
304:, and
11658:Trend
11187:prior
11129:anova
11018:-test
10992:-test
10984:-test
10891:Power
10836:Pivot
10629:shape
10624:scale
10074:Shape
10054:Range
9999:Heinz
9974:Cubic
9910:Index
9830:S2CID
9670:S2CID
9604:S2CID
9547:17â18
5281:is a
4138:(see
3616:is a
3272:) of
3106:With
647:with
574:with
269:is a
11891:Test
11091:Sign
10943:Wald
10016:Mode
9954:Mean
9782:ISBN
9740:ISBN
9698:ISBN
9660:ISBN
9627:ISBN
9522:ISBN
9489:ISBN
9135:and
9095:and
9000:and
8698:and
8616:and
8322:For
7283:are
7088:and
6516:Let
6280:and
6069:and
5961:and
5884:and
5679:and
5542:and
5516:are
5456:and
5189:and
5064:and
4521:and
4491:and
4423:and
4360:For
4225:and
4165:and
3683:and
3313:and
3219:and
3129:and
2977:and
2839:and
1459:and
1247:and
1225:lag.
886:and
800:and
670:and
620:and
478:and
360:and
323:and
231:and
11071:BIC
11066:AIC
9822:doi
9732:doi
9652:doi
9594:doi
9561:hdl
9551:doi
9518:401
8829:and
8752:In
8729:of
8725:is
8401:is
5675:In
5396:If
4499:of
3596:If
3176:In
3153:of
2586:mod
2357:mod
2241:mod
1522:to
1439:If
1416:by
1395:lag
1347:at
1307:at
1223:or
1170:of
600:If
530:of
434:of
319:In
280:or
261:In
12195::
9828:.
9820:.
9810:16
9808:.
9738:.
9682:^
9668:.
9658:.
9602:.
9590:32
9584:.
9559:.
9549:.
9520:.
9487:.
9226:.
9072:.
9033:.
8749:.
8651:,
7737:.
6096:is
5840:.
5667:.
5388:.
5110:.
4265::
4142:).
4131:).
2909:.
2434:,
1436:.
858:.
300:,
296:,
292:,
288:,
265:,
11016:G
10990:F
10982:t
10970:Z
10689:V
10684:U
9886:e
9879:t
9872:v
9836:.
9824::
9816::
9790:.
9748:.
9734::
9706:.
9676:.
9654::
9635:.
9610:.
9596::
9569:.
9563::
9553::
9530:.
9497:.
9330:)
9327:y
9324:,
9321:x
9318:(
9315:t
9312:)
9309:y
9306:,
9303:x
9300:(
9297:f
9289:t
9279:f
9270:1
9263:y
9260:,
9257:x
9247:n
9244:1
9203:T
9183:F
9163:1
9143:T
9123:F
9103:t
9083:f
9060:]
9057:1
9054:,
9051:1
9045:[
9029:L
8978:,
8941:T
8934:T
8929:,
8920:F
8913:F
8884:t
8873:)
8870:y
8867:,
8864:x
8861:(
8858:t
8855:=
8852:)
8849:y
8846:,
8843:x
8840:(
8837:T
8815:f
8804:)
8801:y
8798:,
8795:x
8792:(
8789:f
8786:=
8783:)
8780:y
8777:,
8774:x
8771:(
8768:F
8737:f
8711:f
8686:f
8664:f
8639:)
8636:y
8633:,
8630:x
8627:(
8624:f
8604:)
8601:y
8598:,
8595:x
8592:(
8589:t
8569:n
8545:)
8539:t
8528:)
8525:y
8522:,
8519:x
8516:(
8513:t
8509:(
8504:)
8498:f
8487:)
8484:y
8481:,
8478:x
8475:(
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8468:(
8459:t
8449:f
8440:1
8433:y
8430:,
8427:x
8417:n
8414:1
8389:)
8386:y
8383:,
8380:x
8377:(
8374:f
8354:)
8351:y
8348:,
8345:x
8342:(
8339:t
8302:)
8299:)
8296:t
8293:(
8290:)
8287:g
8281:f
8278:(
8275:(
8268:R
8261:t
8256:x
8253:a
8250:m
8246:g
8243:r
8240:a
8234:=
8228:y
8225:a
8222:l
8219:e
8216:d
8161:)
8152:(
8144:X
8141:Y
8137:R
8130:=
8127:)
8121:(
8113:Y
8110:X
8106:R
8079:)
8074:1
8070:t
8066:,
8061:2
8057:t
8053:(
8045:X
8042:Y
8038:R
8031:=
8028:)
8023:2
8019:t
8015:,
8010:1
8006:t
8002:(
7994:Y
7991:X
7987:R
7944:Y
7934:X
7923:]
7913:)
7907:Y
7891:+
7888:t
7884:Y
7879:(
7872:)
7866:X
7853:t
7849:X
7844:(
7839:[
7832:E
7826:=
7818:Y
7808:X
7798:)
7792:(
7784:Y
7781:X
7777:K
7770:=
7767:)
7761:(
7756:Y
7753:X
7721:]
7718:1
7715:,
7712:1
7706:[
7684:X
7681:X
7653:)
7648:2
7644:t
7640:(
7635:X
7627:)
7622:1
7618:t
7614:(
7609:X
7598:]
7588:)
7580:2
7576:t
7560:2
7556:t
7551:X
7546:(
7539:)
7531:1
7527:t
7511:1
7507:t
7502:X
7497:(
7492:[
7485:E
7479:=
7473:)
7468:2
7464:t
7460:(
7455:X
7447:)
7442:1
7438:t
7434:(
7429:X
7419:)
7414:2
7410:t
7406:,
7401:1
7397:t
7393:(
7385:X
7382:X
7378:K
7371:=
7368:)
7363:2
7359:t
7355:,
7350:1
7346:t
7342:(
7337:X
7334:X
7271:)
7266:t
7262:Y
7258:,
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7249:X
7245:(
7225:t
7201:]
7195:[
7189:E
7169:)
7164:t
7160:Y
7156:(
7136:)
7131:t
7127:X
7123:(
7101:X
7074:X
7048:]
7038:)
7032:Y
7019:t
7015:Y
7010:(
7003:)
6997:X
6978:t
6974:X
6969:(
6964:[
6957:E
6954:=
6951:)
6945:(
6937:Y
6934:X
6930:K
6908:]
6898:)
6892:Y
6876:+
6873:t
6869:Y
6864:(
6857:)
6851:X
6838:t
6834:X
6829:(
6824:[
6817:E
6808:)
6802:(
6794:Y
6791:X
6787:K
6759:]
6748:t
6744:Y
6730:t
6726:X
6721:[
6714:E
6711:=
6708:)
6702:(
6694:Y
6691:X
6687:R
6665:]
6651:+
6648:t
6644:Y
6636:t
6632:X
6627:[
6620:E
6611:)
6605:(
6597:Y
6594:X
6590:R
6550:)
6545:t
6541:Y
6537:,
6532:t
6528:X
6524:(
6495:]
6485:)
6482:)
6477:2
6473:t
6469:(
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6436:(
6429:)
6425:)
6420:1
6416:t
6412:(
6407:X
6392:1
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6373:[
6366:E
6357:)
6352:2
6348:t
6344:,
6339:1
6335:t
6331:(
6323:Y
6320:X
6316:K
6307::
6293:2
6289:t
6266:1
6262:t
6229:E
6208:]
6195:2
6191:t
6186:Y
6176:1
6172:t
6167:X
6162:[
6155:E
6146:)
6141:2
6137:t
6133:,
6128:1
6124:t
6120:(
6112:Y
6109:X
6105:R
6082:2
6078:t
6055:1
6051:t
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5987:t
5984:(
5979:2
5974:Y
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5946:t
5943:(
5938:2
5933:X
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5905:t
5902:(
5897:Y
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5869:t
5866:(
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5716:t
5712:Y
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5703:t
5699:X
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5648:H
5623:]
5617:H
5611:W
5605:Z
5601:[
5595:E
5583:W
5578:Z
5573:R
5551:W
5529:Z
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5499:n
5495:W
5491:,
5485:,
5480:1
5476:W
5472:(
5469:=
5465:W
5444:)
5439:m
5435:Z
5431:,
5425:,
5420:1
5416:Z
5412:(
5409:=
5405:Z
5376:]
5371:j
5367:Y
5361:i
5357:X
5353:[
5347:E
5327:)
5324:j
5321:,
5318:i
5315:(
5295:2
5289:3
5266:Y
5261:X
5256:R
5234:)
5228:2
5224:Y
5220:,
5215:1
5211:Y
5206:(
5202:=
5198:Y
5176:)
5170:3
5166:X
5162:,
5157:2
5153:X
5149:,
5144:1
5140:X
5135:(
5131:=
5127:X
5094:E
5073:Y
5051:X
5028:]
5022:]
5017:n
5013:Y
5007:m
5003:X
4999:[
4993:E
4983:]
4978:2
4974:Y
4968:m
4964:X
4960:[
4954:E
4949:]
4944:1
4940:Y
4934:m
4930:X
4926:[
4920:E
4885:]
4880:n
4876:Y
4870:2
4866:X
4862:[
4856:E
4846:]
4841:2
4837:Y
4831:2
4827:X
4823:[
4817:E
4812:]
4807:1
4803:Y
4797:2
4793:X
4789:[
4783:E
4773:]
4768:n
4764:Y
4758:1
4754:X
4750:[
4744:E
4734:]
4729:2
4725:Y
4719:1
4715:X
4711:[
4705:E
4700:]
4695:1
4691:Y
4685:1
4681:X
4677:[
4671:E
4665:[
4660:=
4654:Y
4649:X
4644:R
4623:n
4617:m
4596:]
4591:Y
4586:X
4581:[
4574:E
4562:Y
4557:X
4552:R
4530:Y
4508:X
4471:)
4466:n
4462:Y
4458:,
4452:,
4447:1
4443:Y
4439:(
4436:=
4432:Y
4411:)
4406:m
4402:X
4398:,
4392:,
4387:1
4383:X
4379:(
4376:=
4372:X
4337:.
4325:h
4318:)
4314:f
4308:g
4304:(
4300:=
4296:)
4292:h
4286:f
4282:(
4275:g
4253:h
4233:f
4213:g
4193:g
4173:h
4153:f
4104:}
4100:)
4097:t
4094:(
4091:f
4087:{
4081:F
4073:=
4069:}
4060:)
4057:t
4051:(
4048:f
4042:{
4036:F
4014:f
3989:f
3961:F
3938:,
3934:}
3931:g
3928:{
3922:F
3907:}
3904:f
3901:{
3895:F
3887:=
3883:}
3879:g
3873:f
3869:{
3863:F
3845:.
3832:)
3828:g
3822:g
3818:(
3810:)
3806:f
3800:f
3796:(
3792:=
3788:)
3784:g
3778:f
3774:(
3766:)
3762:g
3756:f
3752:(
3741:.
3729:f
3723:g
3720:=
3717:g
3711:f
3691:g
3671:f
3649:.
3646:g
3640:f
3637:=
3634:g
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