2824:
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5344:
25:
5382:
5370:
762:
351:
503:
231:
1724:
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and boundedly complete, is necessarily minimal sufficient. Another form of
Bahadur's theorem states that any sufficient and boundedly complete statistic over a finite-dimensional coordinate space is also minimal sufficient.
141:. While an ancillary statistic contains no information about the model parameters, a complete statistic contains only information about the parameters, and no ancillary information. It is closely related to the concept of a
1811:
2334:
2095:
1044:
1605:
1482:
467:
1350:
2148:
1902:
1171:
757:{\displaystyle \operatorname {E} _{p}(g(T))=\sum _{t=0}^{n}{g(t){n \choose t}p^{t}(1-p)^{n-t}}=(1-p)^{n}\sum _{t=0}^{n}{g(t){n \choose t}\left({\frac {p}{1-p}}\right)^{t}}.}
824:
1986:
2029:
2206:
2171:
346:{\displaystyle {\text{if }}\operatorname {E} _{\theta }(g(T))=0{\text{ for all }}\theta {\text{ then }}\mathbf {P} _{\theta }(g(T)=0)=1{\text{ for all }}\theta .}
1530:
1384:
2577:
1620:
2339:
832:
2946:
2465:
If there is a minimal sufficient statistic then any complete sufficient statistic is also minimal sufficient. But there are pathological cases where a
2512:
loss function; in many practical applications with the squared loss-function, it has a smaller mean squared error among any estimators with the same
1735:
2242:
4479:
4984:
2743:"An Example of an Improvable RaoâBlackwell Improvement, Inefficient Maximum Likelihood Estimator, and Unbiased Generalized Bayes Estimator"
2669:"An Example of an Improvable RaoâBlackwell Improvement, Inefficient Maximum Likelihood Estimator, and Unbiased Generalized Bayes Estimator"
5134:
4758:
3399:
2477:
The notion of completeness has many applications in statistics, particularly in the following two theorems of mathematical statistics.
42:
2041:
89:
61:
4532:
4971:
68:
961:
2956:
2924:
2894:
2615:
1538:
3394:
3094:
1392:
3998:
3146:
2531:
75:
2725:
416:
1272:
4781:
4673:
2867:
2845:
108:
2838:
57:
5386:
4959:
4833:
2100:
2970:
5017:
4678:
4423:
3794:
3384:
2630:
Young, G. A. and Smith, R. L. (2005). Essentials of
Statistical Inference. (p. 94). Cambridge University Press.
1830:
5068:
4280:
4087:
3976:
3934:
1088:
It is important to notice that the result that all coefficients must be 0 was obtained because of the range of
46:
4008:
2489:
5311:
4270:
3173:
2650:
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4811:
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4655:
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4320:
4275:
4105:
2799:
5408:
5374:
5206:
5007:
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4232:
3986:
3655:
3119:
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4806:
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4471:
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4359:
4070:
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3371:
3243:
2887:
Statistical information and likelihood : A collection of critical essays by Dr. D. Basu
1122:
4823:
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4312:
4237:
4166:
4095:
4015:
4003:
3861:
3854:
3562:
3283:
82:
2919:(Second (updated printing 2007) of the Holden-Day 1976 ed.). Pearson Prentice–Hall.
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4550:
4335:
3777:
3686:
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3557:
3248:
3087:
2832:
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2336:
is a minimal sufficient statistic and is a function of any other minimal sufficient statistic, but
1255:
778:
5215:
4828:
4768:
4705:
4343:
4327:
4065:
3927:
3917:
3767:
3681:
35:
5253:
5183:
4976:
4913:
4668:
4555:
3552:
3449:
3356:
3235:
3134:
2849:
1945:
402:
1991:
5278:
5220:
5163:
4989:
4882:
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4401:
4260:
4252:
4142:
4134:
3949:
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3823:
3782:
3747:
3714:
3660:
3635:
3590:
3529:
3489:
3291:
3114:
2176:
478:
5201:
4776:
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4701:
4663:
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4512:
4391:
4369:
4338:
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4124:
4075:
3993:
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3922:
3878:
3640:
3416:
3296:
3065:
3018:
2966:
2934:
2904:
2554:
2217:
142:
2639:
Casella, G. and Berger, R. L. (2001). Statistical
Inference. (pp. 285â286). Duxbury Press.
2153:
1092:. Had the parameter space been finite and with a number of elements less than or equal to
8:
5348:
5273:
5196:
4877:
4641:
4634:
4596:
4504:
4484:
4456:
4189:
4055:
4050:
4040:
4032:
3850:
3811:
3701:
3691:
3600:
3379:
3335:
3253:
3178:
3080:
2562:
1259:
1223:
1112:= 1 and the parameter space is {0.5}, a single observation and a single parameter value,
190:
138:
134:
1988:
is sufficient but not complete. It admits a non-zero unbiased estimator of zero, namely
1719:{\displaystyle \int _{-\infty }^{\infty }g(x)\exp \left(-(x-2\theta )^{2}/4\right)\,dx.}
5362:
5173:
5027:
4923:
4872:
4748:
4645:
4629:
4606:
4383:
4117:
4100:
4060:
3971:
3866:
3828:
3799:
3759:
3719:
3665:
3582:
3268:
3263:
3053:
3006:
2951:. Springer Texts in Statistics (Third ed.). New York: Springer. pp. xiv+784.
2767:
2742:
2693:
2668:
2581:
2466:
1515:
1369:
2789:
Casella, G. and Berger, R. L. (2001). Statistical
Inference. (pp. 287). Duxbury Press.
1931:) is zero almost everywhere. The exponential is not zero, so this can only happen if
145:
which contains all of the information that the dataset provides about the parameters.
5357:
5268:
5238:
5230:
5050:
5041:
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4897:
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4713:
4601:
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4408:
4396:
4022:
3939:
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3806:
3650:
3572:
3351:
3225:
2987:
2952:
2942:
2920:
2890:
2772:
2721:
2698:
2611:
2546:
1912:
137:
in relation to a parametric model of the dataset. It is opposed to the concept of an
2451:{\displaystyle 2\left(\sum _{i=1}^{n}X_{i}\right)^{2}-(n+1)\sum _{i=1}^{n}X_{i}^{2}}
933:{\displaystyle \sum _{t=0}^{n}g(t){n \choose t}\left({\frac {p}{1-p}}\right)^{t}=0.}
5293:
5248:
5012:
4999:
4892:
4867:
4801:
4733:
4611:
4219:
4112:
4045:
3958:
3905:
3724:
3595:
3389:
3273:
3188:
3155:
3043:
2996:
2762:
2754:
2688:
2680:
161:
3027:
2979:
2758:
2684:
5210:
4954:
4816:
4743:
4418:
4292:
4265:
4242:
4211:
3838:
3833:
3787:
3517:
3168:
3061:
3048:
3031:
3014:
3001:
2983:
2962:
2930:
2912:
2900:
2509:
1366:
To show this, it is sufficient to demonstrate that there is no non-zero function
154:
4700:
5159:
5154:
3617:
3547:
3193:
2513:
1073:
and, therefore, can only be identical to 0 if all coefficients are 0, that is,
1054:
5402:
5316:
5283:
5146:
5107:
4918:
4887:
4351:
4305:
3910:
3612:
3439:
3203:
3198:
385:
1806:{\displaystyle k(\theta )\int _{-\infty }^{\infty }h(x)e^{x\theta }\,dx\,\!}
5258:
5191:
5168:
5083:
4413:
3709:
3607:
3542:
3484:
3469:
3406:
3361:
2776:
2702:
2329:{\displaystyle \left(\sum _{i=1}^{n}X_{i},\sum _{i=1}^{n}X_{i}^{2}\right)}
5301:
5263:
4946:
4847:
4709:
4522:
4489:
3981:
3898:
3893:
3537:
3494:
3474:
3454:
3444:
3213:
3057:
3010:
4147:
3627:
3327:
3258:
3208:
3183:
3103:
2585:
1066:
122:
4300:
4152:
3772:
3567:
3479:
3464:
3459:
3424:
2882:
2523:
then several alternative statistics exist for unbiased estimation of
2508:. In other words, this statistic has a smaller expected loss for any
186:
130:
24:
3816:
3434:
3311:
3306:
3301:
1494:
That fact may be seen as follows. The probability distribution of
5321:
5022:
2917:
Mathematical statistics, Volume 1: Basic and selected topics
2090:{\textstyle X\sim \operatorname {Uniform} (\theta -1,\theta +1).}
2220:
does not exist (for example, see Galili and
Meilijson 2016 ).
5243:
4224:
4198:
4178:
3429:
3220:
2519:
Examples exists that when the minimal sufficient statistic is
2033:
3072:
3032:"Completeness, similar regions, and unbiased estimation. II"
2984:"Completeness, similar regions, and unbiased estimation. I."
2469:
statistic does not exist even if a complete statistic does.
3163:
2740:
2666:
1096:, it might be possible to solve the linear equations in
1039:{\displaystyle \sum _{t=0}^{n}g(t){n \choose t}r^{t}=0.}
368:
if this implication holds for every measurable function
2889:. Lecture Notes in Statistics. Vol. 45. Springer.
2504:, then it is the best mean-unbiased estimator for
2527:, while some of them have lower variance than others.
2179:
2156:
2103:
2044:
1994:
1948:
1600:{\displaystyle \exp \left(-(x-2\theta )^{2}/4\right).}
420:
2492:, which states that if a statistic that is unbiased,
2342:
2245:
1833:
1738:
1623:
1541:
1518:
1512:
and variance 2. Its probability density function in
1395:
1372:
1275:
1125:
964:
835:
781:
506:
419:
380:
The
Bernoulli model admits a complete statistic. Let
234:
4985:
Autoregressive conditional heteroskedasticity (ARCH)
2211:
1477:{\displaystyle g(s(X_{1},X_{2}))=g(X_{1}+X_{2})\,\!}
1116:
is not complete. Observe that, with the definition:
1108:
and get solutions different from 0. For example, if
49:. Unsourced material may be challenged and removed.
4447:
2450:
2328:
2200:
2165:
2142:
2089:
2023:
1980:
1896:
1805:
1718:
1599:
1524:
1476:
1378:
1344:
1165:
1038:
932:
818:
756:
461:
345:
1893:
1802:
1473:
1341:
1014:
1001:
885:
872:
711:
698:
591:
578:
462:{\displaystyle \textstyle T=\sum _{i=1}^{n}X_{i}}
413:be the number of 1s observed in the sample, i.e.
5400:
1345:{\displaystyle s((X_{1},X_{2}))=X_{1}+X_{2}\,\!}
497:is a complete statistic. To see this, note that
4533:Multivariate adaptive regression splines (MARS)
3025:
2977:
2580:. In the case where there exists at least one
2143:{\textstyle \operatorname {E} (\sin(\pi X))=0}
3088:
2715:
2605:
2549:, which states that a statistic that is both
2472:
2462:, so there cannot be a complete statistic.
2911:
1258:, identically distributed random variables,
160:whose probability distribution belongs to a
2941:
2741:Tal Galili; Isaac Meilijson (31 Mar 2016).
2667:Tal Galili; Isaac Meilijson (31 Mar 2016).
2034:Example: Location of a uniform distribution
375:
3133:
3095:
3081:
2716:Casella, George; Berger, Roger L. (2001).
2606:Casella, George; Berger, Roger W. (2001).
2480:
1897:{\displaystyle h(x)=g(x)e^{-x^{2}/4}.\,\!}
1614:above would therefore be a constant times
1203:
3746:
3047:
3036:SankhyÄ: The Indian Journal of Statistics
3000:
2988:SankhyÄ: the Indian Journal of Statistics
2868:Learn how and when to remove this message
2766:
2692:
2216:For some parametric families, a complete
1923:), and cannot be identically zero unless
1892:
1801:
1794:
1706:
1472:
1340:
1208:This example will show that, in a sample
1162:
1104:) obtained by substituting the values of
109:Learn how and when to remove this message
2831:This article includes a list of general
2223:For example, if you take a sample sized
1487:remains zero regardless of the value of
5401:
5059:KaplanâMeier estimator (product limit)
5132:
4699:
4446:
3745:
3515:
3132:
3076:
2800:"Statistical Inference Lecture Notes"
2709:
1240:is complete and sufficient. Suppose (
5369:
5069:Accelerated failure time (AFT) model
2881:
2817:
2568:
47:adding citations to reliable sources
18:
5381:
4664:Analysis of variance (ANOVA, anova)
3516:
2532:minimum-variance unbiased estimator
1226:with known variance, the statistic
13:
4759:CochranâMantelâHaenszel statistics
3385:Pearson product-moment correlation
2837:it lacks sufficient corresponding
2648:
2104:
1764:
1759:
1637:
1632:
1005:
876:
702:
582:
508:
241:
222:if, for every measurable function
14:
5420:
2651:"Uniqueness of Laplace Transform"
2537:
2212:Relation to sufficient statistics
1729:A bit of algebra reduces this to
1049:First, observe that the range of
5380:
5368:
5356:
5343:
5342:
5133:
2822:
2584:statistic, a statistic which is
2458:has an expectation of 0 for all
1166:{\displaystyle g(t)=2(t-0.5),\,}
292:
189:; that is, the composition of a
23:
5018:Least-squares spectral analysis
2720:(2nd ed.). Duxbury Press.
34:needs additional citations for
3999:Mean-unbiased minimum-variance
3102:
2948:Testing statistical hypotheses
2792:
2783:
2734:
2660:
2642:
2633:
2624:
2599:
2409:
2397:
2195:
2186:
2131:
2128:
2119:
2110:
2081:
2057:
1975:
1949:
1858:
1852:
1843:
1837:
1778:
1772:
1748:
1742:
1684:
1668:
1651:
1645:
1572:
1556:
1469:
1443:
1434:
1431:
1405:
1399:
1311:
1308:
1282:
1279:
1156:
1144:
1135:
1129:
995:
989:
866:
860:
807:
804:
798:
792:
692:
686:
652:
639:
620:
607:
572:
566:
535:
532:
526:
520:
489:). If the parameter space for
323:
314:
308:
302:
268:
265:
259:
253:
58:"Completeness" statistics
1:
5312:Geographic information system
4528:Simultaneous equations models
2813:
2759:10.1080/00031305.2015.1100683
2685:10.1080/00031305.2015.1100683
1939:) is zero almost everywhere.
1532:is therefore proportional to
1386:such that the expectation of
1081:) = 0 for all
819:{\displaystyle E_{p}(g(T))=0}
148:
4495:Coefficient of determination
4106:Uniformly most powerful test
3049:10.1007/978-1-4614-1412-4_24
3002:10.1007/978-1-4614-1412-4_23
2945:; Romano, Joseph P. (2005).
1508:is normal with expectation 2
7:
5064:Proportional hazards models
5008:Spectral density estimation
4990:Vector autoregression (VAR)
4424:Maximum posterior estimator
3656:Randomized controlled trial
2915:; Doksum, Kjell A. (2001).
2885:(1988). J. K. Ghosh (ed.).
2150:regardless of the value of
1942:By contrast, the statistic
10:
5425:
4824:Multivariate distributions
3244:Average absolute deviation
2473:Importance of completeness
1981:{\textstyle (X_{1},X_{2})}
767:Observe also that neither
5338:
5292:
5229:
5182:
5145:
5141:
5128:
5100:
5082:
5049:
5040:
4998:
4945:
4906:
4855:
4846:
4812:Structural equation model
4767:
4724:
4720:
4695:
4654:
4620:
4574:
4541:
4503:
4470:
4466:
4442:
4382:
4291:
4210:
4174:
4165:
4148:Score/Lagrange multiplier
4133:
4086:
4031:
3957:
3948:
3758:
3754:
3741:
3700:
3674:
3626:
3581:
3563:Sample size determination
3528:
3524:
3511:
3415:
3370:
3344:
3326:
3282:
3234:
3154:
3145:
3141:
3128:
3110:
2747:The American Statistician
2673:The American Statistician
2227: > 2 from a
2024:{\textstyle X_{1}-X_{2}.}
5307:Environmental statistics
4829:Elliptical distributions
4622:Generalized linear model
4551:Simple linear regression
4321:HodgesâLehmann estimator
3778:Probability distribution
3687:Stochastic approximation
3249:Coefficient of variation
2592:
2201:{\textstyle \sin(\pi X)}
1266:and variance 1. The sum
771:nor 1 −
376:Example: Bernoulli model
364:for the distribution of
218:for the distribution of
4967:Cross-correlation (XCF)
4575:Non-standard predictors
4009:LehmannâScheffĂŠ theorem
3682:Adaptive clinical trial
2852:more precise citations.
2490:LehmannâScheffĂŠ theorem
2481:LehmannâScheffĂŠ theorem
1204:Example: Sum of normals
5363:Mathematics portal
5184:Engineering statistics
5092:NelsonâAalen estimator
4669:Analysis of covariance
4556:Ordinary least squares
4480:Pearson product-moment
3884:Statistical functional
3795:Empirical distribution
3628:Controlled experiments
3357:Frequency distribution
3135:Descriptive statistics
2452:
2432:
2372:
2330:
2305:
2271:
2202:
2167:
2144:
2091:
2025:
1982:
1898:
1824:) is nowhere zero and
1807:
1720:
1601:
1526:
1478:
1380:
1346:
1167:
1040:
985:
947:/(1 −
934:
856:
820:
758:
681:
561:
463:
447:
403:Bernoulli distribution
372:that is also bounded.
347:
5279:Population statistics
5221:System identification
4955:Autocorrelation (ACF)
4883:Exponential smoothing
4797:Discriminant analysis
4792:Canonical correlation
4656:Partition of variance
4518:Regression validation
4362:(JonckheereâTerpstra)
4261:Likelihood-ratio test
3950:Frequentist inference
3862:Locationâscale family
3783:Sampling distribution
3748:Statistical inference
3715:Cross-sectional study
3702:Observational studies
3661:Randomized experiment
3490:Stem-and-leaf display
3292:Central limit theorem
2718:Statistical Inference
2608:Statistical inference
2453:
2412:
2352:
2331:
2285:
2251:
2239:) distribution, then
2203:
2168:
2166:{\textstyle \theta .}
2145:
2092:
2026:
1983:
1899:
1808:
1721:
1602:
1527:
1479:
1381:
1347:
1168:
1041:
965:
935:
836:
821:
759:
661:
541:
479:binomial distribution
464:
427:
348:
193:with a random sample
174:parametrized by
5202:Probabilistic design
4787:Principal components
4630:Exponential families
4582:Nonlinear regression
4561:General linear model
4523:Mixed effects models
4513:Errors and residuals
4490:Confounding variable
4392:Bayesian probability
4370:Van der Waerden test
4360:Ordered alternative
4125:Multiple comparisons
4004:RaoâBlackwellization
3967:Estimating equations
3923:Statistical distance
3641:Factorial experiment
3174:Arithmetic-Geometric
2574:Bounded completeness
2543:Bounded completeness
2340:
2243:
2218:sufficient statistic
2177:
2154:
2101:
2042:
1992:
1946:
1911:this is a two-sided
1831:
1736:
1621:
1539:
1516:
1393:
1370:
1273:
1260:normally distributed
1123:
962:
833:
779:
504:
417:
232:
143:sufficient statistic
43:improve this article
5274:Official statistics
5197:Methods engineering
4878:Seasonal adjustment
4646:Poisson regressions
4566:Bayesian regression
4505:Regression analysis
4485:Partial correlation
4457:Regression analysis
4056:Prediction interval
4051:Likelihood interval
4041:Confidence interval
4033:Interval estimation
3994:Unbiased estimators
3812:Model specification
3692:Up-and-down designs
3380:Partial correlation
3336:Index of dispersion
3254:Interquartile range
2563:ancillary statistic
2500:for some parameter
2447:
2320:
1768:
1641:
1610:The expectation of
1224:normal distribution
334: for all
279: for all
191:measurable function
139:ancillary statistic
129:is a property of a
5409:Statistical theory
5294:Spatial statistics
5174:Medical statistics
5074:First hitting time
5028:Whittle likelihood
4679:Degrees of freedom
4674:Multivariate ANOVA
4607:Heteroscedasticity
4419:Bayesian estimator
4384:Bayesian inference
4233:KolmogorovâSmirnov
4118:Randomization test
4088:Testing hypotheses
4061:Tolerance interval
3972:Maximum likelihood
3867:Exponential family
3800:Density estimation
3760:Statistical theory
3720:Natural experiment
3666:Scientific control
3583:Survey methodology
3269:Standard deviation
2582:minimal sufficient
2551:boundedly complete
2467:minimal sufficient
2448:
2433:
2326:
2306:
2198:
2163:
2140:
2087:
2021:
1978:
1894:
1803:
1751:
1716:
1624:
1597:
1522:
1474:
1376:
1357:complete statistic
1342:
1163:
1036:
930:
816:
754:
473:is a statistic of
459:
458:
362:boundedly complete
343:
5396:
5395:
5334:
5333:
5330:
5329:
5269:National accounts
5239:Actuarial science
5231:Social statistics
5124:
5123:
5120:
5119:
5116:
5115:
5051:Survival function
5036:
5035:
4898:Granger causality
4739:Contingency table
4714:Survival analysis
4691:
4690:
4687:
4686:
4543:Linear regression
4438:
4437:
4434:
4433:
4409:Credible interval
4378:
4377:
4161:
4160:
3977:Method of moments
3846:Parametric family
3807:Statistical model
3737:
3736:
3733:
3732:
3651:Random assignment
3573:Statistical power
3507:
3506:
3503:
3502:
3352:Contingency table
3322:
3321:
3189:Generalized/power
2958:978-0-387-98864-1
2926:978-0-13-850363-5
2896:978-0-387-96751-6
2878:
2877:
2870:
2617:978-1-032-59303-6
2578:Bahadur's theorem
2569:Bahadur's theorem
2208:is not complete.
1913:Laplace transform
1907:As a function of
1525:{\displaystyle x}
1379:{\displaystyle g}
1262:with expectation
1222:of size 2 from a
1012:
912:
883:
738:
709:
589:
481:with parameters (
335:
288:
280:
238:
119:
118:
111:
93:
5416:
5384:
5383:
5372:
5371:
5361:
5360:
5346:
5345:
5249:Crime statistics
5143:
5142:
5130:
5129:
5047:
5046:
5013:Fourier analysis
5000:Frequency domain
4980:
4927:
4893:Structural break
4853:
4852:
4802:Cluster analysis
4749:Log-linear model
4722:
4721:
4697:
4696:
4638:
4612:Homoscedasticity
4468:
4467:
4444:
4443:
4363:
4355:
4347:
4346:(KruskalâWallis)
4331:
4316:
4271:Cross validation
4256:
4238:AndersonâDarling
4185:
4172:
4171:
4143:Likelihood-ratio
4135:Parametric tests
4113:Permutation test
4096:1- & 2-tails
3987:Minimum distance
3959:Point estimation
3955:
3954:
3906:Optimal decision
3857:
3756:
3755:
3743:
3742:
3725:Quasi-experiment
3675:Adaptive designs
3526:
3525:
3513:
3512:
3390:Rank correlation
3152:
3151:
3143:
3142:
3130:
3129:
3097:
3090:
3083:
3074:
3073:
3069:
3051:
3022:
3004:
2974:
2969:. Archived from
2938:
2913:Bickel, Peter J.
2908:
2873:
2866:
2862:
2859:
2853:
2848:this article by
2839:inline citations
2826:
2825:
2818:
2807:
2806:
2804:
2796:
2790:
2787:
2781:
2780:
2770:
2738:
2732:
2731:
2713:
2707:
2706:
2696:
2664:
2658:
2657:
2655:
2649:Orloff, Jeremy.
2646:
2640:
2637:
2631:
2628:
2622:
2621:
2603:
2457:
2455:
2454:
2449:
2446:
2441:
2431:
2426:
2393:
2392:
2387:
2383:
2382:
2381:
2371:
2366:
2335:
2333:
2332:
2327:
2325:
2321:
2319:
2314:
2304:
2299:
2281:
2280:
2270:
2265:
2207:
2205:
2204:
2199:
2172:
2170:
2169:
2164:
2149:
2147:
2146:
2141:
2096:
2094:
2093:
2088:
2030:
2028:
2027:
2022:
2017:
2016:
2004:
2003:
1987:
1985:
1984:
1979:
1974:
1973:
1961:
1960:
1903:
1901:
1900:
1895:
1888:
1887:
1883:
1878:
1877:
1812:
1810:
1809:
1804:
1793:
1792:
1767:
1762:
1725:
1723:
1722:
1717:
1705:
1701:
1697:
1692:
1691:
1640:
1635:
1606:
1604:
1603:
1598:
1593:
1589:
1585:
1580:
1579:
1531:
1529:
1528:
1523:
1483:
1481:
1480:
1475:
1468:
1467:
1455:
1454:
1430:
1429:
1417:
1416:
1385:
1383:
1382:
1377:
1351:
1349:
1348:
1343:
1339:
1338:
1326:
1325:
1307:
1306:
1294:
1293:
1184:)) = 0 although
1172:
1170:
1169:
1164:
1045:
1043:
1042:
1037:
1029:
1028:
1019:
1018:
1017:
1004:
984:
979:
939:
937:
936:
931:
923:
922:
917:
913:
911:
897:
890:
889:
888:
875:
855:
850:
826:if and only if:
825:
823:
822:
817:
791:
790:
775:can be 0. Hence
763:
761:
760:
755:
750:
749:
748:
743:
739:
737:
723:
716:
715:
714:
701:
680:
675:
660:
659:
635:
634:
633:
606:
605:
596:
595:
594:
581:
560:
555:
516:
515:
468:
466:
465:
460:
457:
456:
446:
441:
352:
350:
349:
344:
336:
333:
301:
300:
295:
289:
287: then
286:
281:
278:
249:
248:
239:
236:
162:parametric model
114:
107:
103:
100:
94:
92:
51:
27:
19:
5424:
5423:
5419:
5418:
5417:
5415:
5414:
5413:
5399:
5398:
5397:
5392:
5355:
5326:
5288:
5225:
5211:quality control
5178:
5160:Clinical trials
5137:
5112:
5096:
5084:Hazard function
5078:
5032:
4994:
4978:
4941:
4937:BreuschâGodfrey
4925:
4902:
4842:
4817:Factor analysis
4763:
4744:Graphical model
4716:
4683:
4650:
4636:
4616:
4570:
4537:
4499:
4462:
4461:
4430:
4374:
4361:
4353:
4345:
4329:
4314:
4293:Rank statistics
4287:
4266:Model selection
4254:
4212:Goodness of fit
4206:
4183:
4157:
4129:
4082:
4027:
4016:Median unbiased
3944:
3855:
3788:Order statistic
3750:
3729:
3696:
3670:
3622:
3577:
3520:
3518:Data collection
3499:
3411:
3366:
3340:
3318:
3278:
3230:
3147:Continuous data
3137:
3124:
3106:
3101:
3026:Lehmann, E.L.;
2978:Lehmann, E.L.;
2959:
2927:
2897:
2874:
2863:
2857:
2854:
2844:Please help to
2843:
2827:
2823:
2816:
2811:
2810:
2805:. July 7, 2022.
2802:
2798:
2797:
2793:
2788:
2784:
2739:
2735:
2728:
2714:
2710:
2665:
2661:
2653:
2647:
2643:
2638:
2634:
2629:
2625:
2618:
2604:
2600:
2595:
2576:also occurs in
2571:
2540:
2483:
2475:
2442:
2437:
2427:
2416:
2388:
2377:
2373:
2367:
2356:
2351:
2347:
2346:
2341:
2338:
2337:
2315:
2310:
2300:
2289:
2276:
2272:
2266:
2255:
2250:
2246:
2244:
2241:
2240:
2214:
2178:
2175:
2174:
2155:
2152:
2151:
2102:
2099:
2098:
2043:
2040:
2039:
2036:
2012:
2008:
1999:
1995:
1993:
1990:
1989:
1969:
1965:
1956:
1952:
1947:
1944:
1943:
1879:
1873:
1869:
1865:
1861:
1832:
1829:
1828:
1785:
1781:
1763:
1755:
1737:
1734:
1733:
1693:
1687:
1683:
1664:
1660:
1636:
1628:
1622:
1619:
1618:
1581:
1575:
1571:
1552:
1548:
1540:
1537:
1536:
1517:
1514:
1513:
1507:
1500:
1463:
1459:
1450:
1446:
1425:
1421:
1412:
1408:
1394:
1391:
1390:
1371:
1368:
1367:
1334:
1330:
1321:
1317:
1302:
1298:
1289:
1285:
1274:
1271:
1270:
1253:
1246:
1239:
1232:
1221:
1214:
1206:
1192:) is not 0 for
1124:
1121:
1120:
1024:
1020:
1013:
1000:
999:
998:
980:
969:
963:
960:
959:
918:
901:
896:
892:
891:
884:
871:
870:
869:
851:
840:
834:
831:
830:
786:
782:
780:
777:
776:
744:
727:
722:
718:
717:
710:
697:
696:
695:
682:
676:
665:
655:
651:
623:
619:
601:
597:
590:
577:
576:
575:
562:
556:
545:
511:
507:
505:
502:
501:
493:is (0,1), then
452:
448:
442:
431:
418:
415:
414:
405:with parameter
400:
392:such that each
378:
332:
296:
291:
290:
285:
277:
244:
240:
235:
233:
230:
229:
206:
199:
173:
155:random variable
151:
115:
104:
98:
95:
52:
50:
40:
28:
17:
16:Statistics term
12:
11:
5:
5422:
5412:
5411:
5394:
5393:
5391:
5390:
5378:
5366:
5352:
5339:
5336:
5335:
5332:
5331:
5328:
5327:
5325:
5324:
5319:
5314:
5309:
5304:
5298:
5296:
5290:
5289:
5287:
5286:
5281:
5276:
5271:
5266:
5261:
5256:
5251:
5246:
5241:
5235:
5233:
5227:
5226:
5224:
5223:
5218:
5213:
5204:
5199:
5194:
5188:
5186:
5180:
5179:
5177:
5176:
5171:
5166:
5157:
5155:Bioinformatics
5151:
5149:
5139:
5138:
5126:
5125:
5122:
5121:
5118:
5117:
5114:
5113:
5111:
5110:
5104:
5102:
5098:
5097:
5095:
5094:
5088:
5086:
5080:
5079:
5077:
5076:
5071:
5066:
5061:
5055:
5053:
5044:
5038:
5037:
5034:
5033:
5031:
5030:
5025:
5020:
5015:
5010:
5004:
5002:
4996:
4995:
4993:
4992:
4987:
4982:
4974:
4969:
4964:
4963:
4962:
4960:partial (PACF)
4951:
4949:
4943:
4942:
4940:
4939:
4934:
4929:
4921:
4916:
4910:
4908:
4907:Specific tests
4904:
4903:
4901:
4900:
4895:
4890:
4885:
4880:
4875:
4870:
4865:
4859:
4857:
4850:
4844:
4843:
4841:
4840:
4839:
4838:
4837:
4836:
4821:
4820:
4819:
4809:
4807:Classification
4804:
4799:
4794:
4789:
4784:
4779:
4773:
4771:
4765:
4764:
4762:
4761:
4756:
4754:McNemar's test
4751:
4746:
4741:
4736:
4730:
4728:
4718:
4717:
4693:
4692:
4689:
4688:
4685:
4684:
4682:
4681:
4676:
4671:
4666:
4660:
4658:
4652:
4651:
4649:
4648:
4632:
4626:
4624:
4618:
4617:
4615:
4614:
4609:
4604:
4599:
4594:
4592:Semiparametric
4589:
4584:
4578:
4576:
4572:
4571:
4569:
4568:
4563:
4558:
4553:
4547:
4545:
4539:
4538:
4536:
4535:
4530:
4525:
4520:
4515:
4509:
4507:
4501:
4500:
4498:
4497:
4492:
4487:
4482:
4476:
4474:
4464:
4463:
4460:
4459:
4454:
4448:
4440:
4439:
4436:
4435:
4432:
4431:
4429:
4428:
4427:
4426:
4416:
4411:
4406:
4405:
4404:
4399:
4388:
4386:
4380:
4379:
4376:
4375:
4373:
4372:
4367:
4366:
4365:
4357:
4349:
4333:
4330:(MannâWhitney)
4325:
4324:
4323:
4310:
4309:
4308:
4297:
4295:
4289:
4288:
4286:
4285:
4284:
4283:
4278:
4273:
4263:
4258:
4255:(ShapiroâWilk)
4250:
4245:
4240:
4235:
4230:
4222:
4216:
4214:
4208:
4207:
4205:
4204:
4196:
4187:
4175:
4169:
4167:Specific tests
4163:
4162:
4159:
4158:
4156:
4155:
4150:
4145:
4139:
4137:
4131:
4130:
4128:
4127:
4122:
4121:
4120:
4110:
4109:
4108:
4098:
4092:
4090:
4084:
4083:
4081:
4080:
4079:
4078:
4073:
4063:
4058:
4053:
4048:
4043:
4037:
4035:
4029:
4028:
4026:
4025:
4020:
4019:
4018:
4013:
4012:
4011:
4006:
3991:
3990:
3989:
3984:
3979:
3974:
3963:
3961:
3952:
3946:
3945:
3943:
3942:
3937:
3932:
3931:
3930:
3920:
3915:
3914:
3913:
3903:
3902:
3901:
3896:
3891:
3881:
3876:
3871:
3870:
3869:
3864:
3859:
3843:
3842:
3841:
3836:
3831:
3821:
3820:
3819:
3814:
3804:
3803:
3802:
3792:
3791:
3790:
3780:
3775:
3770:
3764:
3762:
3752:
3751:
3739:
3738:
3735:
3734:
3731:
3730:
3728:
3727:
3722:
3717:
3712:
3706:
3704:
3698:
3697:
3695:
3694:
3689:
3684:
3678:
3676:
3672:
3671:
3669:
3668:
3663:
3658:
3653:
3648:
3643:
3638:
3632:
3630:
3624:
3623:
3621:
3620:
3618:Standard error
3615:
3610:
3605:
3604:
3603:
3598:
3587:
3585:
3579:
3578:
3576:
3575:
3570:
3565:
3560:
3555:
3550:
3548:Optimal design
3545:
3540:
3534:
3532:
3522:
3521:
3509:
3508:
3505:
3504:
3501:
3500:
3498:
3497:
3492:
3487:
3482:
3477:
3472:
3467:
3462:
3457:
3452:
3447:
3442:
3437:
3432:
3427:
3421:
3419:
3413:
3412:
3410:
3409:
3404:
3403:
3402:
3397:
3387:
3382:
3376:
3374:
3368:
3367:
3365:
3364:
3359:
3354:
3348:
3346:
3345:Summary tables
3342:
3341:
3339:
3338:
3332:
3330:
3324:
3323:
3320:
3319:
3317:
3316:
3315:
3314:
3309:
3304:
3294:
3288:
3286:
3280:
3279:
3277:
3276:
3271:
3266:
3261:
3256:
3251:
3246:
3240:
3238:
3232:
3231:
3229:
3228:
3223:
3218:
3217:
3216:
3211:
3206:
3201:
3196:
3191:
3186:
3181:
3179:Contraharmonic
3176:
3171:
3160:
3158:
3149:
3139:
3138:
3126:
3125:
3123:
3122:
3117:
3111:
3108:
3107:
3100:
3099:
3092:
3085:
3077:
3071:
3070:
3042:(3): 219â236.
3023:
2995:(4): 305â340.
2975:
2973:on 2013-02-02.
2957:
2943:E. L., Lehmann
2939:
2925:
2909:
2895:
2876:
2875:
2830:
2828:
2821:
2815:
2812:
2809:
2808:
2791:
2782:
2753:(1): 108â113.
2733:
2727:978-0534243128
2726:
2708:
2679:(1): 108â113.
2659:
2641:
2632:
2623:
2616:
2597:
2596:
2594:
2591:
2570:
2567:
2547:Basu's theorem
2539:
2538:Basu's theorem
2536:
2514:expected value
2488:occurs in the
2482:
2479:
2474:
2471:
2445:
2440:
2436:
2430:
2425:
2422:
2419:
2415:
2411:
2408:
2405:
2402:
2399:
2396:
2391:
2386:
2380:
2376:
2370:
2365:
2362:
2359:
2355:
2350:
2345:
2324:
2318:
2313:
2309:
2303:
2298:
2295:
2292:
2288:
2284:
2279:
2275:
2269:
2264:
2261:
2258:
2254:
2249:
2213:
2210:
2197:
2194:
2191:
2188:
2185:
2182:
2162:
2159:
2139:
2136:
2133:
2130:
2127:
2124:
2121:
2118:
2115:
2112:
2109:
2106:
2086:
2083:
2080:
2077:
2074:
2071:
2068:
2065:
2062:
2059:
2056:
2053:
2050:
2047:
2035:
2032:
2020:
2015:
2011:
2007:
2002:
1998:
1977:
1972:
1968:
1964:
1959:
1955:
1951:
1905:
1904:
1891:
1886:
1882:
1876:
1872:
1868:
1864:
1860:
1857:
1854:
1851:
1848:
1845:
1842:
1839:
1836:
1814:
1813:
1800:
1797:
1791:
1788:
1784:
1780:
1777:
1774:
1771:
1766:
1761:
1758:
1754:
1750:
1747:
1744:
1741:
1727:
1726:
1715:
1712:
1709:
1704:
1700:
1696:
1690:
1686:
1682:
1679:
1676:
1673:
1670:
1667:
1663:
1659:
1656:
1653:
1650:
1647:
1644:
1639:
1634:
1631:
1627:
1608:
1607:
1596:
1592:
1588:
1584:
1578:
1574:
1570:
1567:
1564:
1561:
1558:
1555:
1551:
1547:
1544:
1521:
1505:
1498:
1485:
1484:
1471:
1466:
1462:
1458:
1453:
1449:
1445:
1442:
1439:
1436:
1433:
1428:
1424:
1420:
1415:
1411:
1407:
1404:
1401:
1398:
1375:
1353:
1352:
1337:
1333:
1329:
1324:
1320:
1316:
1313:
1310:
1305:
1301:
1297:
1292:
1288:
1284:
1281:
1278:
1251:
1244:
1237:
1230:
1219:
1212:
1205:
1202:
1174:
1173:
1161:
1158:
1155:
1152:
1149:
1146:
1143:
1140:
1137:
1134:
1131:
1128:
1055:positive reals
1047:
1046:
1035:
1032:
1027:
1023:
1016:
1011:
1008:
1003:
997:
994:
991:
988:
983:
978:
975:
972:
968:
941:
940:
929:
926:
921:
916:
910:
907:
904:
900:
895:
887:
882:
879:
874:
868:
865:
862:
859:
854:
849:
846:
843:
839:
815:
812:
809:
806:
803:
800:
797:
794:
789:
785:
765:
764:
753:
747:
742:
736:
733:
730:
726:
721:
713:
708:
705:
700:
694:
691:
688:
685:
679:
674:
671:
668:
664:
658:
654:
650:
647:
644:
641:
638:
632:
629:
626:
622:
618:
615:
612:
609:
604:
600:
593:
588:
585:
580:
574:
571:
568:
565:
559:
554:
551:
548:
544:
540:
537:
534:
531:
528:
525:
522:
519:
514:
510:
455:
451:
445:
440:
437:
434:
430:
426:
423:
396:
377:
374:
360:is said to be
356:The statistic
354:
353:
342:
339:
331:
328:
325:
322:
319:
316:
313:
310:
307:
304:
299:
294:
284:
276:
273:
270:
267:
264:
261:
258:
255:
252:
247:
243:
214:is said to be
210:The statistic
204:
197:
169:
150:
147:
135:sample dataset
133:computed on a
117:
116:
31:
29:
22:
15:
9:
6:
4:
3:
2:
5421:
5410:
5407:
5406:
5404:
5389:
5388:
5379:
5377:
5376:
5367:
5365:
5364:
5359:
5353:
5351:
5350:
5341:
5340:
5337:
5323:
5320:
5318:
5317:Geostatistics
5315:
5313:
5310:
5308:
5305:
5303:
5300:
5299:
5297:
5295:
5291:
5285:
5284:Psychometrics
5282:
5280:
5277:
5275:
5272:
5270:
5267:
5265:
5262:
5260:
5257:
5255:
5252:
5250:
5247:
5245:
5242:
5240:
5237:
5236:
5234:
5232:
5228:
5222:
5219:
5217:
5214:
5212:
5208:
5205:
5203:
5200:
5198:
5195:
5193:
5190:
5189:
5187:
5185:
5181:
5175:
5172:
5170:
5167:
5165:
5161:
5158:
5156:
5153:
5152:
5150:
5148:
5147:Biostatistics
5144:
5140:
5136:
5131:
5127:
5109:
5108:Log-rank test
5106:
5105:
5103:
5099:
5093:
5090:
5089:
5087:
5085:
5081:
5075:
5072:
5070:
5067:
5065:
5062:
5060:
5057:
5056:
5054:
5052:
5048:
5045:
5043:
5039:
5029:
5026:
5024:
5021:
5019:
5016:
5014:
5011:
5009:
5006:
5005:
5003:
5001:
4997:
4991:
4988:
4986:
4983:
4981:
4979:(BoxâJenkins)
4975:
4973:
4970:
4968:
4965:
4961:
4958:
4957:
4956:
4953:
4952:
4950:
4948:
4944:
4938:
4935:
4933:
4932:DurbinâWatson
4930:
4928:
4922:
4920:
4917:
4915:
4914:DickeyâFuller
4912:
4911:
4909:
4905:
4899:
4896:
4894:
4891:
4889:
4888:Cointegration
4886:
4884:
4881:
4879:
4876:
4874:
4871:
4869:
4866:
4864:
4863:Decomposition
4861:
4860:
4858:
4854:
4851:
4849:
4845:
4835:
4832:
4831:
4830:
4827:
4826:
4825:
4822:
4818:
4815:
4814:
4813:
4810:
4808:
4805:
4803:
4800:
4798:
4795:
4793:
4790:
4788:
4785:
4783:
4780:
4778:
4775:
4774:
4772:
4770:
4766:
4760:
4757:
4755:
4752:
4750:
4747:
4745:
4742:
4740:
4737:
4735:
4734:Cohen's kappa
4732:
4731:
4729:
4727:
4723:
4719:
4715:
4711:
4707:
4703:
4698:
4694:
4680:
4677:
4675:
4672:
4670:
4667:
4665:
4662:
4661:
4659:
4657:
4653:
4647:
4643:
4639:
4633:
4631:
4628:
4627:
4625:
4623:
4619:
4613:
4610:
4608:
4605:
4603:
4600:
4598:
4595:
4593:
4590:
4588:
4587:Nonparametric
4585:
4583:
4580:
4579:
4577:
4573:
4567:
4564:
4562:
4559:
4557:
4554:
4552:
4549:
4548:
4546:
4544:
4540:
4534:
4531:
4529:
4526:
4524:
4521:
4519:
4516:
4514:
4511:
4510:
4508:
4506:
4502:
4496:
4493:
4491:
4488:
4486:
4483:
4481:
4478:
4477:
4475:
4473:
4469:
4465:
4458:
4455:
4453:
4450:
4449:
4445:
4441:
4425:
4422:
4421:
4420:
4417:
4415:
4412:
4410:
4407:
4403:
4400:
4398:
4395:
4394:
4393:
4390:
4389:
4387:
4385:
4381:
4371:
4368:
4364:
4358:
4356:
4350:
4348:
4342:
4341:
4340:
4337:
4336:Nonparametric
4334:
4332:
4326:
4322:
4319:
4318:
4317:
4311:
4307:
4306:Sample median
4304:
4303:
4302:
4299:
4298:
4296:
4294:
4290:
4282:
4279:
4277:
4274:
4272:
4269:
4268:
4267:
4264:
4262:
4259:
4257:
4251:
4249:
4246:
4244:
4241:
4239:
4236:
4234:
4231:
4229:
4227:
4223:
4221:
4218:
4217:
4215:
4213:
4209:
4203:
4201:
4197:
4195:
4193:
4188:
4186:
4181:
4177:
4176:
4173:
4170:
4168:
4164:
4154:
4151:
4149:
4146:
4144:
4141:
4140:
4138:
4136:
4132:
4126:
4123:
4119:
4116:
4115:
4114:
4111:
4107:
4104:
4103:
4102:
4099:
4097:
4094:
4093:
4091:
4089:
4085:
4077:
4074:
4072:
4069:
4068:
4067:
4064:
4062:
4059:
4057:
4054:
4052:
4049:
4047:
4044:
4042:
4039:
4038:
4036:
4034:
4030:
4024:
4021:
4017:
4014:
4010:
4007:
4005:
4002:
4001:
4000:
3997:
3996:
3995:
3992:
3988:
3985:
3983:
3980:
3978:
3975:
3973:
3970:
3969:
3968:
3965:
3964:
3962:
3960:
3956:
3953:
3951:
3947:
3941:
3938:
3936:
3933:
3929:
3926:
3925:
3924:
3921:
3919:
3916:
3912:
3911:loss function
3909:
3908:
3907:
3904:
3900:
3897:
3895:
3892:
3890:
3887:
3886:
3885:
3882:
3880:
3877:
3875:
3872:
3868:
3865:
3863:
3860:
3858:
3852:
3849:
3848:
3847:
3844:
3840:
3837:
3835:
3832:
3830:
3827:
3826:
3825:
3822:
3818:
3815:
3813:
3810:
3809:
3808:
3805:
3801:
3798:
3797:
3796:
3793:
3789:
3786:
3785:
3784:
3781:
3779:
3776:
3774:
3771:
3769:
3766:
3765:
3763:
3761:
3757:
3753:
3749:
3744:
3740:
3726:
3723:
3721:
3718:
3716:
3713:
3711:
3708:
3707:
3705:
3703:
3699:
3693:
3690:
3688:
3685:
3683:
3680:
3679:
3677:
3673:
3667:
3664:
3662:
3659:
3657:
3654:
3652:
3649:
3647:
3644:
3642:
3639:
3637:
3634:
3633:
3631:
3629:
3625:
3619:
3616:
3614:
3613:Questionnaire
3611:
3609:
3606:
3602:
3599:
3597:
3594:
3593:
3592:
3589:
3588:
3586:
3584:
3580:
3574:
3571:
3569:
3566:
3564:
3561:
3559:
3556:
3554:
3551:
3549:
3546:
3544:
3541:
3539:
3536:
3535:
3533:
3531:
3527:
3523:
3519:
3514:
3510:
3496:
3493:
3491:
3488:
3486:
3483:
3481:
3478:
3476:
3473:
3471:
3468:
3466:
3463:
3461:
3458:
3456:
3453:
3451:
3448:
3446:
3443:
3441:
3440:Control chart
3438:
3436:
3433:
3431:
3428:
3426:
3423:
3422:
3420:
3418:
3414:
3408:
3405:
3401:
3398:
3396:
3393:
3392:
3391:
3388:
3386:
3383:
3381:
3378:
3377:
3375:
3373:
3369:
3363:
3360:
3358:
3355:
3353:
3350:
3349:
3347:
3343:
3337:
3334:
3333:
3331:
3329:
3325:
3313:
3310:
3308:
3305:
3303:
3300:
3299:
3298:
3295:
3293:
3290:
3289:
3287:
3285:
3281:
3275:
3272:
3270:
3267:
3265:
3262:
3260:
3257:
3255:
3252:
3250:
3247:
3245:
3242:
3241:
3239:
3237:
3233:
3227:
3224:
3222:
3219:
3215:
3212:
3210:
3207:
3205:
3202:
3200:
3197:
3195:
3192:
3190:
3187:
3185:
3182:
3180:
3177:
3175:
3172:
3170:
3167:
3166:
3165:
3162:
3161:
3159:
3157:
3153:
3150:
3148:
3144:
3140:
3136:
3131:
3127:
3121:
3118:
3116:
3113:
3112:
3109:
3105:
3098:
3093:
3091:
3086:
3084:
3079:
3078:
3075:
3067:
3063:
3059:
3055:
3050:
3045:
3041:
3037:
3033:
3029:
3024:
3020:
3016:
3012:
3008:
3003:
2998:
2994:
2990:
2989:
2985:
2981:
2976:
2972:
2968:
2964:
2960:
2954:
2950:
2949:
2944:
2940:
2936:
2932:
2928:
2922:
2918:
2914:
2910:
2906:
2902:
2898:
2892:
2888:
2884:
2880:
2879:
2872:
2869:
2861:
2858:February 2012
2851:
2847:
2841:
2840:
2834:
2829:
2820:
2819:
2801:
2795:
2786:
2778:
2774:
2769:
2764:
2760:
2756:
2752:
2748:
2744:
2737:
2729:
2723:
2719:
2712:
2704:
2700:
2695:
2690:
2686:
2682:
2678:
2674:
2670:
2663:
2652:
2645:
2636:
2627:
2619:
2613:
2610:. CRC Press.
2609:
2602:
2598:
2590:
2587:
2583:
2579:
2575:
2566:
2564:
2560:
2556:
2552:
2548:
2544:
2535:
2533:
2528:
2526:
2522:
2517:
2515:
2511:
2507:
2503:
2499:
2495:
2491:
2487:
2478:
2470:
2468:
2463:
2461:
2443:
2438:
2434:
2428:
2423:
2420:
2417:
2413:
2406:
2403:
2400:
2394:
2389:
2384:
2378:
2374:
2368:
2363:
2360:
2357:
2353:
2348:
2343:
2322:
2316:
2311:
2307:
2301:
2296:
2293:
2290:
2286:
2282:
2277:
2273:
2267:
2262:
2259:
2256:
2252:
2247:
2238:
2234:
2230:
2226:
2221:
2219:
2209:
2192:
2189:
2183:
2180:
2160:
2157:
2137:
2134:
2125:
2122:
2116:
2113:
2107:
2084:
2078:
2075:
2072:
2069:
2066:
2063:
2060:
2054:
2051:
2048:
2045:
2031:
2018:
2013:
2009:
2005:
2000:
1996:
1970:
1966:
1962:
1957:
1953:
1940:
1938:
1934:
1930:
1926:
1922:
1918:
1914:
1910:
1889:
1884:
1880:
1874:
1870:
1866:
1862:
1855:
1849:
1846:
1840:
1834:
1827:
1826:
1825:
1823:
1819:
1798:
1795:
1789:
1786:
1782:
1775:
1769:
1756:
1752:
1745:
1739:
1732:
1731:
1730:
1713:
1710:
1707:
1702:
1698:
1694:
1688:
1680:
1677:
1674:
1671:
1665:
1661:
1657:
1654:
1648:
1642:
1629:
1625:
1617:
1616:
1615:
1613:
1594:
1590:
1586:
1582:
1576:
1568:
1565:
1562:
1559:
1553:
1549:
1545:
1542:
1535:
1534:
1533:
1519:
1511:
1504:
1501: +
1497:
1492:
1490:
1464:
1460:
1456:
1451:
1447:
1440:
1437:
1426:
1422:
1418:
1413:
1409:
1402:
1396:
1389:
1388:
1387:
1373:
1364:
1362:
1358:
1335:
1331:
1327:
1322:
1318:
1314:
1303:
1299:
1295:
1290:
1286:
1276:
1269:
1268:
1267:
1265:
1261:
1257:
1250:
1243:
1236:
1233: +
1229:
1225:
1218:
1211:
1201:
1199:
1195:
1191:
1187:
1183:
1179:
1159:
1153:
1150:
1147:
1141:
1138:
1132:
1126:
1119:
1118:
1117:
1115:
1111:
1107:
1103:
1099:
1095:
1091:
1086:
1084:
1080:
1076:
1072:
1068:
1064:
1060:
1056:
1052:
1033:
1030:
1025:
1021:
1009:
1006:
992:
986:
981:
976:
973:
970:
966:
958:
957:
956:
954:
950:
946:
927:
924:
919:
914:
908:
905:
902:
898:
893:
880:
877:
863:
857:
852:
847:
844:
841:
837:
829:
828:
827:
813:
810:
801:
795:
787:
783:
774:
770:
751:
745:
740:
734:
731:
728:
724:
719:
706:
703:
689:
683:
677:
672:
669:
666:
662:
656:
648:
645:
642:
636:
630:
627:
624:
616:
613:
610:
602:
598:
586:
583:
569:
563:
557:
552:
549:
546:
542:
538:
529:
523:
517:
512:
500:
499:
498:
496:
492:
488:
484:
480:
477:which has a
476:
472:
453:
449:
443:
438:
435:
432:
428:
424:
421:
412:
408:
404:
401:has the same
399:
395:
391:
387:
386:random sample
383:
373:
371:
367:
363:
359:
340:
337:
329:
326:
320:
317:
311:
305:
297:
282:
274:
271:
262:
256:
250:
245:
228:
227:
226:
225:
221:
217:
213:
208:
203:
196:
192:
188:
184:
179:
177:
172:
168:
167:
163:
159:
156:
146:
144:
140:
136:
132:
128:
124:
113:
110:
102:
91:
88:
84:
81:
77:
74:
70:
67:
63:
60: â
59:
55:
54:Find sources:
48:
44:
38:
37:
32:This article
30:
26:
21:
20:
5385:
5373:
5354:
5347:
5259:Econometrics
5209: /
5192:Chemometrics
5169:Epidemiology
5162: /
5135:Applications
4977:ARIMA model
4924:Q-statistic
4873:Stationarity
4769:Multivariate
4712: /
4708: /
4706:Multivariate
4704: /
4644: /
4640: /
4414:Bayes factor
4313:Signed rank
4225:
4199:
4191:
4179:
3874:Completeness
3873:
3710:Cohort study
3608:Opinion poll
3543:Missing data
3530:Study design
3485:Scatter plot
3407:Scatter plot
3400:Spearman's Ď
3362:Grouped data
3039:
3035:
2992:
2986:
2971:the original
2947:
2916:
2886:
2864:
2855:
2836:
2794:
2785:
2750:
2746:
2736:
2717:
2711:
2676:
2672:
2662:
2644:
2635:
2626:
2607:
2601:
2573:
2572:
2550:
2542:
2541:
2529:
2524:
2521:not complete
2520:
2518:
2505:
2501:
2493:
2486:Completeness
2485:
2484:
2476:
2464:
2459:
2236:
2232:
2228:
2224:
2222:
2215:
2037:
1941:
1936:
1932:
1928:
1924:
1920:
1916:
1908:
1906:
1821:
1817:
1815:
1728:
1611:
1609:
1509:
1502:
1495:
1493:
1488:
1486:
1365:
1360:
1356:
1354:
1263:
1248:
1241:
1234:
1227:
1216:
1209:
1207:
1197:
1196:= 0 nor for
1193:
1189:
1185:
1181:
1177:
1175:
1113:
1109:
1105:
1101:
1097:
1093:
1089:
1087:
1082:
1078:
1074:
1070:
1062:
1058:
1050:
1048:
955:, one gets:
952:
948:
944:
943:On denoting
942:
772:
768:
766:
494:
490:
486:
482:
474:
470:
410:
406:
397:
393:
389:
381:
379:
369:
365:
361:
357:
355:
223:
219:
215:
211:
209:
201:
194:
182:
180:
175:
170:
165:
164:
157:
152:
127:completeness
126:
120:
105:
96:
86:
79:
72:
65:
53:
41:Please help
36:verification
33:
5387:WikiProject
5302:Cartography
5264:Jurimetrics
5216:Reliability
4947:Time domain
4926:(LjungâBox)
4848:Time-series
4726:Categorical
4710:Time-series
4702:Categorical
4637:(Bernoulli)
4472:Correlation
4452:Correlation
4248:JarqueâBera
4220:Chi-squared
3982:M-estimator
3935:Asymptotics
3879:Sufficiency
3646:Interaction
3558:Replication
3538:Effect size
3495:Violin plot
3475:Radar chart
3455:Forest plot
3445:Correlogram
3395:Kendall's Ď
3028:ScheffĂŠ, H.
2980:ScheffĂŠ, H.
2850:introducing
2559:independent
1256:independent
153:Consider a
99:August 2009
5254:Demography
4972:ARMA model
4777:Regression
4354:(Friedman)
4315:(Wilcoxon)
4253:Normality
4243:Lilliefors
4190:Student's
4066:Resampling
3940:Robustness
3928:divergence
3918:Efficiency
3856:(monotone)
3851:Likelihood
3768:Population
3601:Stratified
3553:Population
3372:Dependence
3328:Count data
3259:Percentile
3236:Dispersion
3169:Arithmetic
3104:Statistics
2833:references
2814:References
2586:sufficient
2555:sufficient
2545:occurs in
2498:sufficient
1067:polynomial
1057:. Also, E(
149:Definition
123:statistics
69:newspapers
4635:Logistic
4402:posterior
4328:Rank sum
4076:Jackknife
4071:Bootstrap
3889:Bootstrap
3824:Parameter
3773:Statistic
3568:Statistic
3480:Run chart
3465:Pie chart
3460:Histogram
3450:Fan chart
3425:Bar chart
3307:L-moments
3194:Geometric
2530:See also
2414:∑
2395:−
2354:∑
2287:∑
2253:∑
2190:π
2184:
2158:θ
2123:π
2117:
2108:
2073:θ
2064:−
2061:θ
2055:
2049:∼
2006:−
1867:−
1790:θ
1765:∞
1760:∞
1757:−
1753:∫
1746:θ
1681:θ
1675:−
1666:−
1658:
1638:∞
1633:∞
1630:−
1626:∫
1569:θ
1563:−
1554:−
1546:
1151:−
967:∑
906:−
838:∑
732:−
663:∑
646:−
628:−
614:−
543:∑
518:
429:∑
338:θ
298:θ
283:θ
251:
246:θ
187:statistic
131:statistic
5403:Category
5349:Category
5042:Survival
4919:Johansen
4642:Binomial
4597:Isotonic
4184:(normal)
3829:location
3636:Blocking
3591:Sampling
3470:QâQ plot
3435:Box plot
3417:Graphics
3312:Skewness
3302:Kurtosis
3274:Variance
3204:Heronian
3199:Harmonic
3058:25048243
3030:(1955).
3011:25048038
2982:(1950).
2883:Basu, D.
2777:27499547
2703:27499547
2494:complete
2038:Suppose
1176:then, E(
1065:)) is a
388:of size
237:if
216:complete
5375:Commons
5322:Kriging
5207:Process
5164:studies
5023:Wavelet
4856:General
4023:Plug-in
3817:L space
3596:Cluster
3297:Moments
3115:Outline
3066:0072410
3019:0039201
2967:2135927
2935:0443141
2905:0953081
2846:improve
2768:4960505
2694:4960505
2561:of any
2052:Uniform
1215:,
1053:is the
83:scholar
5244:Census
4834:Normal
4782:Manova
4602:Robust
4352:2-way
4344:1-way
4182:-test
3853:
3430:Biplot
3221:Median
3214:Lehmer
3156:Center
3064:
3056:
3017:
3009:
2965:
2955:
2933:
2923:
2903:
2893:
2835:, but
2775:
2765:
2724:
2701:
2691:
2614:
2510:convex
1816:where
1254:) are
409:. Let
85:
78:
71:
64:
56:
4868:Trend
4397:prior
4339:anova
4228:-test
4202:-test
4194:-test
4101:Power
4046:Pivot
3839:shape
3834:scale
3284:Shape
3264:Range
3209:Heinz
3184:Cubic
3120:Index
3054:JSTOR
3007:JSTOR
2803:(PDF)
2654:(PDF)
2593:Notes
2173:Thus
2097:Then
1355:is a
1200:= 1.
951:) by
384:be a
200:,...,
185:is a
90:JSTOR
76:books
5101:Test
4301:Sign
4153:Wald
3226:Mode
3164:Mean
2953:ISBN
2921:ISBN
2891:ISBN
2773:PMID
2722:ISBN
2699:PMID
2612:ISBN
2553:and
2496:and
1359:for
181:Say
62:news
4281:BIC
4276:AIC
3044:doi
2997:doi
2763:PMC
2755:doi
2689:PMC
2681:doi
2557:is
2181:sin
2114:sin
1915:of
1655:exp
1543:exp
1154:0.5
1069:in
121:In
45:by
5405::
3062:MR
3060:.
3052:.
3040:15
3038:.
3034:.
3015:MR
3013:.
3005:.
2993:10
2991:.
2963:MR
2961:.
2931:MR
2929:.
2901:MR
2899:.
2771:.
2761:.
2751:70
2749:.
2745:.
2697:.
2687:.
2677:70
2675:.
2671:.
2565:.
2534:.
2516:.
1491:.
1363:.
1247:,
1085:.
1034:0.
928:0.
469:.
224:g,
207:.
178:.
125:,
4226:G
4200:F
4192:t
4180:Z
3899:V
3894:U
3096:e
3089:t
3082:v
3068:.
3046::
3021:.
2999::
2937:.
2907:.
2871:)
2865:(
2860:)
2856:(
2842:.
2779:.
2757::
2730:.
2705:.
2683::
2656:.
2620:.
2525:θ
2506:θ
2502:θ
2460:θ
2444:2
2439:i
2435:X
2429:n
2424:1
2421:=
2418:i
2410:)
2407:1
2404:+
2401:n
2398:(
2390:2
2385:)
2379:i
2375:X
2369:n
2364:1
2361:=
2358:i
2349:(
2344:2
2323:)
2317:2
2312:i
2308:X
2302:n
2297:1
2294:=
2291:i
2283:,
2278:i
2274:X
2268:n
2263:1
2260:=
2257:i
2248:(
2237:θ
2235:,
2233:θ
2231:(
2229:N
2225:n
2196:)
2193:X
2187:(
2161:.
2138:0
2135:=
2132:)
2129:)
2126:X
2120:(
2111:(
2105:E
2085:.
2082:)
2079:1
2076:+
2070:,
2067:1
2058:(
2046:X
2019:.
2014:2
2010:X
2001:1
1997:X
1976:)
1971:2
1967:X
1963:,
1958:1
1954:X
1950:(
1937:x
1935:(
1933:g
1929:x
1927:(
1925:h
1921:X
1919:(
1917:h
1909:θ
1890:.
1885:4
1881:/
1875:2
1871:x
1863:e
1859:)
1856:x
1853:(
1850:g
1847:=
1844:)
1841:x
1838:(
1835:h
1822:θ
1820:(
1818:k
1799:x
1796:d
1787:x
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1779:)
1776:x
1773:(
1770:h
1749:)
1743:(
1740:k
1714:.
1711:x
1708:d
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1699:4
1695:/
1689:2
1685:)
1678:2
1672:x
1669:(
1662:(
1652:)
1649:x
1646:(
1643:g
1612:g
1595:.
1591:)
1587:4
1583:/
1577:2
1573:)
1566:2
1560:x
1557:(
1550:(
1520:x
1510:θ
1506:2
1503:X
1499:1
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1489:θ
1470:)
1465:2
1461:X
1457:+
1452:1
1448:X
1444:(
1441:g
1438:=
1435:)
1432:)
1427:2
1423:X
1419:,
1414:1
1410:X
1406:(
1403:s
1400:(
1397:g
1374:g
1361:θ
1336:2
1332:X
1328:+
1323:1
1319:X
1315:=
1312:)
1309:)
1304:2
1300:X
1296:,
1291:1
1287:X
1283:(
1280:(
1277:s
1264:θ
1252:2
1249:X
1245:1
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1235:X
1231:1
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1220:2
1217:X
1213:1
1210:X
1198:t
1194:t
1190:t
1188:(
1186:g
1182:T
1180:(
1178:g
1160:,
1157:)
1148:t
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1139:=
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1133:t
1130:(
1127:g
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1106:r
1102:t
1100:(
1098:g
1094:n
1090:r
1083:t
1079:t
1077:(
1075:g
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1026:t
1022:r
1015:)
1010:t
1007:n
1002:(
996:)
993:t
990:(
987:g
982:n
977:0
974:=
971:t
953:r
949:p
945:p
925:=
920:t
915:)
909:p
903:1
899:p
894:(
886:)
881:t
878:n
873:(
867:)
864:t
861:(
858:g
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845:=
842:t
814:0
811:=
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805:)
802:T
799:(
796:g
793:(
788:p
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773:p
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707:t
704:n
699:(
693:)
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539:=
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521:(
513:p
509:E
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487:p
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321:0
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263:T
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