264:. Examples include the development of multivariate models relating 1) multi-wavelength spectral response to analyte concentration, 2) molecular descriptors to biological activity, 3) multivariate process conditions/states to final product attributes. The process requires a calibration or training data set, which includes reference values for the properties of interest for prediction, and the measured attributes believed to correspond to these properties. For case 1), for example, one can assemble data from a number of samples, including concentrations for an analyte of interest for each sample (the reference) and the corresponding infrared spectrum of that sample. Multivariate calibration techniques such as partial-least squares regression, or principal component regression (and near countless other methods) are then used to construct a mathematical model that relates the multivariate response (spectrum) to the concentration of the analyte of interest, and such a model can be used to efficiently predict the concentrations of new samples.
320:, and spectral unmixing. For example, from a data set comprising fluorescence spectra from a series of samples each containing multiple fluorophores, multivariate curve resolution methods can be used to extract the fluorescence spectra of the individual fluorophores, along with their relative concentrations in each of the samples, essentially unmixing the total fluorescence spectrum into the contributions from the individual components. The problem is usually ill-determined due to rotational ambiguity (many possible solutions can equivalently represent the measured data), so the application of additional constraints is common, such as non-negativity, unimodality, or known interrelationships between the individual components (e.g., kinetic or mass-balance constraints).
276:). Equally important is that multivariate calibration allows for accurate quantitative analysis in the presence of heavy interference by other analytes. The selectivity of the analytical method is provided as much by the mathematical calibration, as the analytical measurement modalities. For example, near-infrared spectra, which are extremely broad and non-selective compared to other analytical techniques (such as infrared or Raman spectra), can often be used successfully in conjunction with carefully developed multivariate calibration methods to predict concentrations of analytes in very complex matrices.
4240:
373:, modeling and optimization accounts for a substantial amount of historical chemometric development. Spectroscopy has been used successfully for online monitoring of manufacturing processes for 30â40 years, and this process data is highly amenable to chemometric modeling. Specifically in terms of MSPC, multiway modeling of batch and continuous processes is increasingly common in industry and remains an active area of research in chemometrics and chemical engineering. Process analytical chemistry as it was originally termed, or the newer term
120:(PLS), orthogonal partial least-squares (OPLS), and two-way orthogonal partial least squares (O2PLS). This is primarily because, while the datasets may be highly multivariate there is strong and often linear low-rank structure present. PCA and PLS have been shown over time very effective at empirically modeling the more chemically interesting low-rank structure, exploiting the interrelationships or 'latent variables' in the data, and providing alternative compact coordinate systems for further numerical analysis such as
268:
and can therefore be considered optimal descriptors, whereas in inverse methods the models are solved to be optimal in predicting the properties of interest (e.g., concentrations, optimal predictors). Inverse methods usually require less physical knowledge of the chemical system, and at least in theory provide superior predictions in the mean-squared error sense, and hence inverse approaches tend to be more frequently applied in contemporary multivariate calibration.
4226:
1902:
1926:
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1938:
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1914:
83:, and the development of improved chemometric methods of analysis also continues to advance the state of the art in analytical instrumentation and methodology. It is an application-driven discipline, and thus while the standard chemometric methodologies are very widely used industrially, academic groups are dedicated to the continued development of chemometric theory, method and application development.
72:
model understanding and identification). In predictive applications, properties of chemical systems are modeled with the intent of predicting new properties or behavior of interest. In both cases, the datasets can be small but are often large and complex, involving hundreds to thousands of variables, and hundreds to thousands of cases or observations.
284:
Supervised multivariate classification techniques are closely related to multivariate calibration techniques in that a calibration or training set is used to develop a mathematical model capable of classifying future samples. The techniques employed in chemometrics are similar to those used in other
315:
In chemometric parlance, multivariate curve resolution seeks to deconstruct data sets with limited or absent reference information and system knowledge. Some of the earliest work on these techniques was done by Lawton and
Sylvestre in the early 1970s. These approaches are also called self-modeling
267:
Techniques in multivariate calibration are often broadly categorized as classical or inverse methods. The principal difference between these approaches is that in classical calibration the models are solved such that they are optimal in describing the measured analytical responses (e.g., spectra)
71:
Chemometrics is applied to solve both descriptive and predictive problems in experimental natural sciences, especially in chemistry. In descriptive applications, properties of chemical systems are modeled with the intent of learning the underlying relationships and structure of the system (i.e.,
358:
in predicting the attribute of interest, and the performance of classifiers as a true-positive rate/false-positive rate pairs (or a full ROC curve). A recent report by
Olivieri et al. provides a comprehensive overview of figures of merit and uncertainty estimation in multivariate calibration,
271:
The main advantages of the use of multivariate calibration techniques is that fast, cheap, or non-destructive analytical measurements (such as optical spectroscopy) can be used to estimate sample properties which would otherwise require time-consuming, expensive or destructive testing (such as
111:
Multivariate analysis was a critical facet even in the earliest applications of chemometrics. Data from infrared and UV/visible spectroscopy are often counted in thousands of measurements per sample. Mass spectrometry, nuclear magnetic resonance, atomic emission/absorption and chromatography
383:
are heavily used in chemometric applications. These are higher-order extensions of more widely used methods. For example, while the analysis of a table (matrix, or second-order array) of data is routine in several fields, multiway methods are applied to data sets that involve 3rd, 4th, or
91:
Although one could argue that even the earliest analytical experiments in chemistry involved a form of chemometrics, the field is generally recognized to have emerged in the 1970s as computers became increasingly exploited for scientific investigation. The term 'chemometrics' was coined by
342:
is also a critical component of almost all chemometric applications, particularly the use of signal pretreatments to condition data prior to calibration or classification. The techniques employed commonly in chemometrics are often closely related to those used in related fields. Signal
333:
remains a core area of study in chemometrics and several monographs are specifically devoted to experimental design in chemical applications. Sound principles of experimental design have been widely adopted within the chemometrics community, although many complex experiments are purely
285:
fields â multivariate discriminant analysis, logistic regression, neural networks, regression/classification trees. The use of rank reduction techniques in conjunction with these conventional classification methods is routine in chemometrics, for example discriminant analysis on
384:
higher-orders. Data of this type is very common in chemistry, for example a liquid-chromatography / mass spectrometry (LC-MS) system generates a large matrix of data (elution time versus m/z) for each sample analyzed. The data across multiple samples thus comprises a
107:
Many early applications involved multivariate classification, numerous quantitative predictive applications followed, and by the late 1970s and early 1980s a wide variety of data- and computer-driven chemical analyses were occurring.
153:. These journals continue to cover both fundamental and methodological research in chemometrics. At present, most routine applications of existing chemometric methods are commonly published in application-oriented journals (e.g.,
22:
is the science of extracting information from chemical systems by data-driven means. Chemometrics is inherently interdisciplinary, using methods frequently employed in core data-analytic disciplines such as
349:
Like most arenas in the physical sciences, chemometrics is quantitatively oriented, so considerable emphasis is placed on performance characterization, model selection, verification & validation, and
307:) is also commonly used to discover patterns in complex data sets, and again many of the core techniques used in chemometrics are common to other fields such as machine learning and statistical learning.
248:. The objective is to develop models which can be used to predict properties of interest based on measured properties of the chemical system, such as pressure, flow, temperature,
1156:
Oliveri, Paolo; Malegori, Cristina; Simonetti, Remo; Casale, Monica (2019). "The impact of signal pre-processing on the final interpretation of analytical outcomes â A tutorial".
388:. Batch process modeling involves data sets that have time vs. process variables vs. batch number. The multiway mathematical methods applied to these sorts of problems include
359:
including multivariate definitions of selectivity, sensitivity, SNR and prediction interval estimation. Chemometric model selection usually involves the use of tools such as
300:, are able to build models for an individual class of interest. Such methods are particularly useful in the case of quality control and authenticity verification of products.
1581:
1849:
1021:
de Juan, A.; Tauler, R. (2003). "Chemometrics
Applied to Unravel Multicomponent Processes and Mixtures. Revisiting Latest Trends in Multivariate Resolution".
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Bro, R.; Workman, J. J.; Mobley, P. R.; Kowalski, B. R. (1997). "Overview of chemometrics applied to spectroscopy: 1985â95, Part 3âMultiway analysis".
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Martin, E. B.; Morris, A. J. (1996). "An overview of multivariate statistical process control in continuous and batch process performance monitoring".
132:. Partial least squares in particular was heavily used in chemometric applications for many years before it began to find regular use in other fields.
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Franke, J. (2002). "Inverse Least
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149:
112:
experiments are also all by nature highly multivariate. The structure of these data was found to be conducive to using techniques such as
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273:
3640:
2281:
1209:"Guidelines for calibration in analytical chemistry Part 3. Uncertainty estimation and figures of merit for multivariate calibration"
3414:
1551:
3853:
334:
observational, and there can be little control over the properties and interrelationships of the samples and sample properties.
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Illman, D. L.; Callis, J. B.; Kowalski, B. R. (1986). "Process
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173:). Several important books/monographs on chemometrics were also first published in the 1980s, including the first edition of
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in a 1971 grant application, and the
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Some large chemometric application areas have gone on to represent new domains, such as molecular modeling and
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pre-processing may affect the way in which outcomes of the final data processing can be interpreted.
104:, Sweden, and Kowalski was a professor of analytical chemistry at University of Washington, Seattle.
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1969:
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Science of extracting information from chemical systems by data-driven means
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General resource on advanced chemometric methods and recent developments
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279:
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Through the 1980s three dedicated journals appeared in the field:
4203:
3904:
389:
169:
48:
1535:
1517:
552:
244:
Many chemical problems and applications of chemometrics involve
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3106:
3080:
3060:
2311:
2102:
1538:
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Chemometric techniques are particularly heavily used in
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3415:Multivariate adaptive regression splines (MARS)
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411:Chemometrics and Intelligent Laboratory Systems
280:Classification, pattern recognition, clustering
144:Chemometrics and Intelligent Laboratory Systems
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605:
1970:
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862:
576:
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1090:
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150:Journal of Chemical Information and Modeling
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1390:Smilde, A. K.; Bro, R.; Geladi, P. (2004).
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1977:
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599:
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462:
303:Unsupervised classification (also termed
1628:
1451:
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435:
905:
401:
4283:
3941:KaplanâMeier estimator (product limit)
1873:Analytical and Bioanalytical Chemistry
1582:Chemometric Analysis for Spectroscopy
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837:
742:
4014:
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1913:
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1454:Applied Chemometrics for Scientists
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3641:CochranâMantelâHaenszel statistics
2267:Pearson product-moment correlation
1436:
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14:
4317:
1545:
1118:Statistical design â chemometrics
4262:
4250:
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4225:
4224:
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1936:
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1901:
1900:
1565:Homepage of Chemometrics, Sweden
181:, Sharaf, Illman and Kowalski's
3900:Least-squares spectral analysis
1475:Practical Guide to Chemometrics
1445:Chemometrics: A Practical Guide
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3410:Simultaneous equations models
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395:
375:process analytical technology
311:Multivariate curve resolution
234:
226:process analytical technology
114:principal components analysis
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3377:Coefficient of determination
2988:Uniformly most powerful test
1502:Chemometrics in Spectroscopy
1407:Applied Spectroscopy Reviews
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179:Factor Analysis in Chemistry
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3946:Proportional hazards models
3890:Spectral density estimation
3872:Vector autoregression (VAR)
3306:Maximum posterior estimator
2538:Randomized controlled trial
1651:Flame emission spectrometer
369:statistical process control
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4322:
3706:Multivariate distributions
2126:Average absolute deviation
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1477:(2nd ed.). CRC Press.
1316:10.1177/014233129601800107
1213:Pure and Applied Chemistry
86:
4220:
4174:
4111:
4064:
4027:
4023:
4010:
3982:
3964:
3931:
3922:
3880:
3827:
3788:
3737:
3728:
3694:Structural equation model
3649:
3606:
3602:
3577:
3536:
3502:
3456:
3423:
3385:
3352:
3348:
3324:
3264:
3173:
3092:
3056:
3047:
3030:Score/Lagrange multiplier
3015:
2968:
2913:
2839:
2830:
2640:
2636:
2623:
2582:
2556:
2508:
2463:
2445:Sample size determination
2410:
2406:
2393:
2297:
2252:
2226:
2208:
2164:
2116:
2036:
2027:
2023:
2010:
1992:
1896:
1847:
1806:
1750:
1727:Ion mobility spectrometry
1717:Electroanalytical methods
1699:
1636:
1560:Glossary for Chemometrics
1465:. 4 volume set. Elsevier.
1427:10.1080/05704929708003315
1178:10.1016/j.aca.2018.10.055
1070:10.1080/10408340600970005
928:10.1016/j.aca.2017.05.013
706:10.1177/00037028221094070
438:J. Chem. Inf. Comput. Sci
208:, the '-omics' fields of
4189:Environmental statistics
3711:Elliptical distributions
3504:Generalized linear model
3433:Simple linear regression
3203:HodgesâLehmann estimator
2660:Probability distribution
2569:Stochastic approximation
2131:Coefficient of variation
1520:Chemometrics: A Textbook
1511:Multivariate Calibration
1452:Brereton, R. G. (2007).
865:Fresenius' J. Anal. Chem
753:10.1002/0470027320.s4603
583:Multivariate Calibration
555:Chemometrics: a textbook
240:Multivariate calibration
191:Multivariate Calibration
187:Chemometrics: a textbook
4291:Computational chemistry
3849:Cross-correlation (XCF)
3457:Non-standard predictors
2891:LehmannâScheffĂ© theorem
2564:Adaptive clinical trial
1887:Analytical Biochemistry
1676:Melting point apparatus
1226:10.1351/pac200678030633
1120:. Amsterdam: Elsevier.
557:. Amsterdam: Elsevier.
469:Journal of Chemometrics
356:root mean squared error
224:, process modeling and
138:Journal of Chemometrics
25:multivariate statistics
4245:Mathematics portal
4066:Engineering statistics
3974:NelsonâAalen estimator
3551:Analysis of covariance
3438:Ordinary least squares
3362:Pearson product-moment
2766:Statistical functional
2677:Empirical distribution
2510:Controlled experiments
2239:Frequency distribution
2017:Descriptive statistics
1866:Analytica Chimica Acta
1158:Analytica Chimica Acta
1023:Analytica Chimica Acta
908:Analytica Chimica Acta
659:10.1002/cem.1180040604
622:10.1002/cem.1180040503
165:Analytica Chimica Acta
4161:Population statistics
4103:System identification
3837:Autocorrelation (ACF)
3765:Exponential smoothing
3679:Discriminant analysis
3674:Canonical correlation
3538:Partition of variance
3400:Regression validation
3244:(JonckheereâTerpstra)
3143:Likelihood-ratio test
2832:Frequentist inference
2744:Locationâscale family
2665:Sampling distribution
2630:Statistical inference
2597:Cross-sectional study
2584:Observational studies
2543:Randomized experiment
2372:Stem-and-leaf display
2174:Central limit theorem
1758:Coning and quartering
1666:Infrared spectrometer
877:10.1007/s002160000556
298:one-class classifiers
291:partial least squares
118:partial least-squares
4301:Analytical chemistry
4084:Probabilistic design
3669:Principal components
3512:Exponential families
3464:Nonlinear regression
3443:General linear model
3405:Mixed effects models
3395:Errors and residuals
3372:Confounding variable
3274:Bayesian probability
3252:Van der Waerden test
3242:Ordered alternative
3007:Multiple comparisons
2886:RaoâBlackwellization
2849:Estimating equations
2805:Statistical distance
2523:Factorial experiment
2056:Arithmetic-Geometric
1880:Analytical Chemistry
1722:Gravimetric analysis
1686:Optical spectrometer
1630:Analytical chemistry
778:Analytical Chemistry
686:Applied Spectroscopy
287:principal components
160:Analytical Chemistry
155:Applied Spectroscopy
77:analytical chemistry
53:chemical engineering
4156:Official statistics
4079:Methods engineering
3760:Seasonal adjustment
3528:Poisson regressions
3448:Bayesian regression
3387:Regression analysis
3367:Partial correlation
3339:Regression analysis
2938:Prediction interval
2933:Likelihood interval
2923:Confidence interval
2915:Interval estimation
2876:Unbiased estimators
2694:Model specification
2574:Up-and-down designs
2262:Partial correlation
2218:Index of dispersion
2136:Interquartile range
1482:Kramer, R. (1998).
1419:1997ApSRv..32..237B
1353:1984Sci...226..312H
1308:1996TIMC...18...51M
1250:American Laboratory
1170:2019AcAC.1058....9O
1035:2003AcAC..500..195D
920:2017AcAC..982....9O
747:. New York: Wiley.
698:2022ApSpe..76.1021B
585:. New York: Wiley.
532:. New York: Wiley.
506:. New York: Wiley.
450:10.1021/ci60004a002
330:Experimental design
130:pattern recognition
29:applied mathematics
4176:Spatial statistics
4056:Medical statistics
3956:First hitting time
3910:Whittle likelihood
3561:Degrees of freedom
3556:Multivariate ANOVA
3489:Heteroscedasticity
3301:Bayesian estimator
3266:Bayesian inference
3115:KolmogorovâSmirnov
3000:Randomization test
2970:Testing hypotheses
2943:Tolerance interval
2854:Maximum likelihood
2749:Exponential family
2682:Density estimation
2642:Statistical theory
2602:Natural experiment
2548:Scientific control
2465:Survey methodology
2151:Standard deviation
1793:Separation process
1788:Sample preparation
1592:2017-09-22 at the
1570:2016-01-20 at the
842:. Boston: Riedel.
316:mixture analysis,
4278:
4277:
4216:
4215:
4212:
4211:
4151:National accounts
4121:Actuarial science
4113:Social statistics
4006:
4005:
4002:
4001:
3998:
3997:
3933:Survival function
3918:
3917:
3780:Granger causality
3621:Contingency table
3596:Survival analysis
3573:
3572:
3569:
3568:
3425:Linear regression
3320:
3319:
3316:
3315:
3291:Credible interval
3260:
3259:
3043:
3042:
2859:Method of moments
2728:Parametric family
2689:Statistical model
2619:
2618:
2615:
2614:
2533:Random assignment
2455:Statistical power
2389:
2388:
2385:
2384:
2234:Contingency table
2204:
2203:
2071:Generalized/power
1952:
1951:
1834:Standard addition
1829:Internal standard
1819:Calibration curve
1732:Mass spectrometry
1691:Spectrophotometer
1671:Mass spectrometer
1656:Gas chromatograph
1527:Otto, M. (2007).
1471:Gemperline, P. J.
1347:(4672): 312â318.
790:10.1021/ac049953w
784:(15): 4364â4373.
339:Signal processing
185:, Massart et al.
4313:
4266:
4265:
4254:
4253:
4243:
4242:
4228:
4227:
4131:Crime statistics
4025:
4024:
4012:
4011:
3929:
3928:
3895:Fourier analysis
3882:Frequency domain
3862:
3809:
3775:Structural break
3735:
3734:
3684:Cluster analysis
3631:Log-linear model
3604:
3603:
3579:
3578:
3520:
3494:Homoscedasticity
3350:
3349:
3326:
3325:
3245:
3237:
3229:
3228:(KruskalâWallis)
3213:
3198:
3153:Cross validation
3138:
3120:AndersonâDarling
3067:
3054:
3053:
3025:Likelihood-ratio
3017:Parametric tests
2995:Permutation test
2978:1- & 2-tails
2869:Minimum distance
2841:Point estimation
2837:
2836:
2788:Optimal decision
2739:
2638:
2637:
2625:
2624:
2607:Quasi-experiment
2557:Adaptive designs
2408:
2407:
2395:
2394:
2272:Rank correlation
2034:
2033:
2025:
2024:
2012:
2011:
1979:
1972:
1965:
1956:
1955:
1940:
1939:
1928:
1916:
1915:
1904:
1903:
1839:Isotope dilution
1623:
1616:
1609:
1600:
1599:
1541:
1532:
1523:
1514:
1505:
1496:
1487:
1478:
1466:
1457:
1448:
1431:
1430:
1402:
1396:
1395:
1387:
1381:
1380:
1334:
1328:
1327:
1291:
1285:
1284:
1264:
1258:
1257:
1245:
1239:
1238:
1228:
1204:
1198:
1197:
1153:
1147:
1146:
1138:
1132:
1131:
1113:
1107:
1106:
1088:
1082:
1081:
1064:(3â4): 163â176.
1053:
1047:
1046:
1029:(1â2): 195â210.
1018:
1012:
1011:
991:
985:
984:
964:
958:
957:
939:
903:
897:
896:
860:
854:
853:
835:
829:
828:
808:
802:
801:
773:
767:
766:
740:
734:
733:
692:(9): 1021â1041.
677:
671:
670:
640:
634:
633:
603:
597:
596:
578:
569:
568:
550:
544:
543:
525:
519:
517:
499:
493:
492:
460:
454:
453:
433:
427:
426:
407:As recounted in
405:
381:Multiway methods
352:figures of merit
324:Other techniques
305:cluster analysis
33:computer science
4321:
4320:
4316:
4315:
4314:
4312:
4311:
4310:
4306:Cheminformatics
4281:
4280:
4279:
4274:
4237:
4208:
4170:
4107:
4093:quality control
4060:
4042:Clinical trials
4019:
3994:
3978:
3966:Hazard function
3960:
3914:
3876:
3860:
3823:
3819:BreuschâGodfrey
3807:
3784:
3724:
3699:Factor analysis
3645:
3626:Graphical model
3598:
3565:
3532:
3518:
3498:
3452:
3419:
3381:
3344:
3343:
3312:
3256:
3243:
3235:
3227:
3211:
3196:
3175:Rank statistics
3169:
3148:Model selection
3136:
3094:Goodness of fit
3088:
3065:
3039:
3011:
2964:
2909:
2898:Median unbiased
2826:
2737:
2670:Order statistic
2632:
2611:
2578:
2552:
2504:
2459:
2402:
2400:Data collection
2381:
2293:
2248:
2222:
2200:
2160:
2112:
2029:Continuous data
2019:
2006:
1988:
1983:
1953:
1948:
1892:
1843:
1802:
1746:
1695:
1638:Instrumentation
1632:
1627:
1594:Wayback Machine
1572:Wayback Machine
1548:
1439:
1437:Further reading
1434:
1403:
1399:
1388:
1384:
1335:
1331:
1292:
1288:
1265:
1261:
1246:
1242:
1205:
1201:
1154:
1150:
1139:
1135:
1128:
1114:
1110:
1103:
1089:
1085:
1054:
1050:
1019:
1015:
992:
988:
965:
961:
904:
900:
861:
857:
850:
836:
832:
809:
805:
774:
770:
763:
741:
737:
678:
674:
646:J. Chemometrics
641:
637:
609:J. Chemometrics
604:
600:
593:
579:
572:
565:
551:
547:
540:
526:
522:
514:
500:
496:
481:10.1002/cem.775
461:
457:
434:
430:
406:
402:
398:
326:
313:
282:
242:
237:
206:cheminformatics
193:by Martens and
102:UmeÄ University
89:
69:
17:
12:
11:
5:
4319:
4309:
4308:
4303:
4298:
4293:
4276:
4275:
4273:
4272:
4260:
4248:
4234:
4221:
4218:
4217:
4214:
4213:
4210:
4209:
4207:
4206:
4201:
4196:
4191:
4186:
4180:
4178:
4172:
4171:
4169:
4168:
4163:
4158:
4153:
4148:
4143:
4138:
4133:
4128:
4123:
4117:
4115:
4109:
4108:
4106:
4105:
4100:
4095:
4086:
4081:
4076:
4070:
4068:
4062:
4061:
4059:
4058:
4053:
4048:
4039:
4037:Bioinformatics
4033:
4031:
4021:
4020:
4008:
4007:
4004:
4003:
4000:
3999:
3996:
3995:
3993:
3992:
3986:
3984:
3980:
3979:
3977:
3976:
3970:
3968:
3962:
3961:
3959:
3958:
3953:
3948:
3943:
3937:
3935:
3926:
3920:
3919:
3916:
3915:
3913:
3912:
3907:
3902:
3897:
3892:
3886:
3884:
3878:
3877:
3875:
3874:
3869:
3864:
3856:
3851:
3846:
3845:
3844:
3842:partial (PACF)
3833:
3831:
3825:
3824:
3822:
3821:
3816:
3811:
3803:
3798:
3792:
3790:
3789:Specific tests
3786:
3785:
3783:
3782:
3777:
3772:
3767:
3762:
3757:
3752:
3747:
3741:
3739:
3732:
3726:
3725:
3723:
3722:
3721:
3720:
3719:
3718:
3703:
3702:
3701:
3691:
3689:Classification
3686:
3681:
3676:
3671:
3666:
3661:
3655:
3653:
3647:
3646:
3644:
3643:
3638:
3636:McNemar's test
3633:
3628:
3623:
3618:
3612:
3610:
3600:
3599:
3575:
3574:
3571:
3570:
3567:
3566:
3564:
3563:
3558:
3553:
3548:
3542:
3540:
3534:
3533:
3531:
3530:
3514:
3508:
3506:
3500:
3499:
3497:
3496:
3491:
3486:
3481:
3476:
3474:Semiparametric
3471:
3466:
3460:
3458:
3454:
3453:
3451:
3450:
3445:
3440:
3435:
3429:
3427:
3421:
3420:
3418:
3417:
3412:
3407:
3402:
3397:
3391:
3389:
3383:
3382:
3380:
3379:
3374:
3369:
3364:
3358:
3356:
3346:
3345:
3342:
3341:
3336:
3330:
3322:
3321:
3318:
3317:
3314:
3313:
3311:
3310:
3309:
3308:
3298:
3293:
3288:
3287:
3286:
3281:
3270:
3268:
3262:
3261:
3258:
3257:
3255:
3254:
3249:
3248:
3247:
3239:
3231:
3215:
3212:(MannâWhitney)
3207:
3206:
3205:
3192:
3191:
3190:
3179:
3177:
3171:
3170:
3168:
3167:
3166:
3165:
3160:
3155:
3145:
3140:
3137:(ShapiroâWilk)
3132:
3127:
3122:
3117:
3112:
3104:
3098:
3096:
3090:
3089:
3087:
3086:
3078:
3069:
3057:
3051:
3049:Specific tests
3045:
3044:
3041:
3040:
3038:
3037:
3032:
3027:
3021:
3019:
3013:
3012:
3010:
3009:
3004:
3003:
3002:
2992:
2991:
2990:
2980:
2974:
2972:
2966:
2965:
2963:
2962:
2961:
2960:
2955:
2945:
2940:
2935:
2930:
2925:
2919:
2917:
2911:
2910:
2908:
2907:
2902:
2901:
2900:
2895:
2894:
2893:
2888:
2873:
2872:
2871:
2866:
2861:
2856:
2845:
2843:
2834:
2828:
2827:
2825:
2824:
2819:
2814:
2813:
2812:
2802:
2797:
2796:
2795:
2785:
2784:
2783:
2778:
2773:
2763:
2758:
2753:
2752:
2751:
2746:
2741:
2725:
2724:
2723:
2718:
2713:
2703:
2702:
2701:
2696:
2686:
2685:
2684:
2674:
2673:
2672:
2662:
2657:
2652:
2646:
2644:
2634:
2633:
2621:
2620:
2617:
2616:
2613:
2612:
2610:
2609:
2604:
2599:
2594:
2588:
2586:
2580:
2579:
2577:
2576:
2571:
2566:
2560:
2558:
2554:
2553:
2551:
2550:
2545:
2540:
2535:
2530:
2525:
2520:
2514:
2512:
2506:
2505:
2503:
2502:
2500:Standard error
2497:
2492:
2487:
2486:
2485:
2480:
2469:
2467:
2461:
2460:
2458:
2457:
2452:
2447:
2442:
2437:
2432:
2430:Optimal design
2427:
2422:
2416:
2414:
2404:
2403:
2391:
2390:
2387:
2386:
2383:
2382:
2380:
2379:
2374:
2369:
2364:
2359:
2354:
2349:
2344:
2339:
2334:
2329:
2324:
2319:
2314:
2309:
2303:
2301:
2295:
2294:
2292:
2291:
2286:
2285:
2284:
2279:
2269:
2264:
2258:
2256:
2250:
2249:
2247:
2246:
2241:
2236:
2230:
2228:
2227:Summary tables
2224:
2223:
2221:
2220:
2214:
2212:
2206:
2205:
2202:
2201:
2199:
2198:
2197:
2196:
2191:
2186:
2176:
2170:
2168:
2162:
2161:
2159:
2158:
2153:
2148:
2143:
2138:
2133:
2128:
2122:
2120:
2114:
2113:
2111:
2110:
2105:
2100:
2099:
2098:
2093:
2088:
2083:
2078:
2073:
2068:
2063:
2061:Contraharmonic
2058:
2053:
2042:
2040:
2031:
2021:
2020:
2008:
2007:
2005:
2004:
1999:
1993:
1990:
1989:
1982:
1981:
1974:
1967:
1959:
1950:
1949:
1947:
1946:
1934:
1922:
1910:
1897:
1894:
1893:
1891:
1890:
1883:
1876:
1869:
1862:
1854:
1852:
1845:
1844:
1842:
1841:
1836:
1831:
1826:
1821:
1816:
1810:
1808:
1804:
1803:
1801:
1800:
1795:
1790:
1785:
1780:
1775:
1770:
1765:
1760:
1754:
1752:
1748:
1747:
1745:
1744:
1739:
1734:
1729:
1724:
1719:
1714:
1712:Chromatography
1709:
1703:
1701:
1697:
1696:
1694:
1693:
1688:
1683:
1678:
1673:
1668:
1663:
1658:
1653:
1648:
1642:
1640:
1634:
1633:
1626:
1625:
1618:
1611:
1603:
1597:
1596:
1584:
1579:
1574:
1562:
1554:
1547:
1546:External links
1544:
1543:
1542:
1533:
1524:
1515:
1506:
1497:
1488:
1479:
1473:, ed. (2006).
1467:
1458:
1449:
1438:
1435:
1433:
1432:
1413:(3): 237â261.
1397:
1382:
1329:
1286:
1275:(3): 403â414.
1259:
1240:
1219:(3): 633â650.
1199:
1148:
1133:
1127:978-0444521811
1126:
1108:
1102:978-0444427342
1101:
1083:
1048:
1013:
1002:(3): 353â368.
986:
975:(3): 617â633.
959:
898:
871:(6): 585â588.
855:
849:978-9027718464
848:
830:
803:
768:
762:978-0471988472
761:
735:
672:
653:(6): 389â412.
635:
616:(5): 337â354.
598:
592:978-0471909798
591:
570:
564:978-0444426604
563:
545:
539:978-0471831068
538:
520:
513:978-0471058816
512:
494:
455:
444:(4): 201â203.
428:
417:(1): 109â115.
399:
397:
394:
325:
322:
312:
309:
281:
278:
241:
238:
236:
233:
98:Bruce Kowalski
88:
85:
68:
65:
15:
9:
6:
4:
3:
2:
4318:
4307:
4304:
4302:
4299:
4297:
4294:
4292:
4289:
4288:
4286:
4271:
4270:
4261:
4259:
4258:
4249:
4247:
4246:
4241:
4235:
4233:
4232:
4223:
4222:
4219:
4205:
4202:
4200:
4199:Geostatistics
4197:
4195:
4192:
4190:
4187:
4185:
4182:
4181:
4179:
4177:
4173:
4167:
4166:Psychometrics
4164:
4162:
4159:
4157:
4154:
4152:
4149:
4147:
4144:
4142:
4139:
4137:
4134:
4132:
4129:
4127:
4124:
4122:
4119:
4118:
4116:
4114:
4110:
4104:
4101:
4099:
4096:
4094:
4090:
4087:
4085:
4082:
4080:
4077:
4075:
4072:
4071:
4069:
4067:
4063:
4057:
4054:
4052:
4049:
4047:
4043:
4040:
4038:
4035:
4034:
4032:
4030:
4029:Biostatistics
4026:
4022:
4018:
4013:
4009:
3991:
3990:Log-rank test
3988:
3987:
3985:
3981:
3975:
3972:
3971:
3969:
3967:
3963:
3957:
3954:
3952:
3949:
3947:
3944:
3942:
3939:
3938:
3936:
3934:
3930:
3927:
3925:
3921:
3911:
3908:
3906:
3903:
3901:
3898:
3896:
3893:
3891:
3888:
3887:
3885:
3883:
3879:
3873:
3870:
3868:
3865:
3863:
3861:(BoxâJenkins)
3857:
3855:
3852:
3850:
3847:
3843:
3840:
3839:
3838:
3835:
3834:
3832:
3830:
3826:
3820:
3817:
3815:
3814:DurbinâWatson
3812:
3810:
3804:
3802:
3799:
3797:
3796:DickeyâFuller
3794:
3793:
3791:
3787:
3781:
3778:
3776:
3773:
3771:
3770:Cointegration
3768:
3766:
3763:
3761:
3758:
3756:
3753:
3751:
3748:
3746:
3745:Decomposition
3743:
3742:
3740:
3736:
3733:
3731:
3727:
3717:
3714:
3713:
3712:
3709:
3708:
3707:
3704:
3700:
3697:
3696:
3695:
3692:
3690:
3687:
3685:
3682:
3680:
3677:
3675:
3672:
3670:
3667:
3665:
3662:
3660:
3657:
3656:
3654:
3652:
3648:
3642:
3639:
3637:
3634:
3632:
3629:
3627:
3624:
3622:
3619:
3617:
3616:Cohen's kappa
3614:
3613:
3611:
3609:
3605:
3601:
3597:
3593:
3589:
3585:
3580:
3576:
3562:
3559:
3557:
3554:
3552:
3549:
3547:
3544:
3543:
3541:
3539:
3535:
3529:
3525:
3521:
3515:
3513:
3510:
3509:
3507:
3505:
3501:
3495:
3492:
3490:
3487:
3485:
3482:
3480:
3477:
3475:
3472:
3470:
3469:Nonparametric
3467:
3465:
3462:
3461:
3459:
3455:
3449:
3446:
3444:
3441:
3439:
3436:
3434:
3431:
3430:
3428:
3426:
3422:
3416:
3413:
3411:
3408:
3406:
3403:
3401:
3398:
3396:
3393:
3392:
3390:
3388:
3384:
3378:
3375:
3373:
3370:
3368:
3365:
3363:
3360:
3359:
3357:
3355:
3351:
3347:
3340:
3337:
3335:
3332:
3331:
3327:
3323:
3307:
3304:
3303:
3302:
3299:
3297:
3294:
3292:
3289:
3285:
3282:
3280:
3277:
3276:
3275:
3272:
3271:
3269:
3267:
3263:
3253:
3250:
3246:
3240:
3238:
3232:
3230:
3224:
3223:
3222:
3219:
3218:Nonparametric
3216:
3214:
3208:
3204:
3201:
3200:
3199:
3193:
3189:
3188:Sample median
3186:
3185:
3184:
3181:
3180:
3178:
3176:
3172:
3164:
3161:
3159:
3156:
3154:
3151:
3150:
3149:
3146:
3144:
3141:
3139:
3133:
3131:
3128:
3126:
3123:
3121:
3118:
3116:
3113:
3111:
3109:
3105:
3103:
3100:
3099:
3097:
3095:
3091:
3085:
3083:
3079:
3077:
3075:
3070:
3068:
3063:
3059:
3058:
3055:
3052:
3050:
3046:
3036:
3033:
3031:
3028:
3026:
3023:
3022:
3020:
3018:
3014:
3008:
3005:
3001:
2998:
2997:
2996:
2993:
2989:
2986:
2985:
2984:
2981:
2979:
2976:
2975:
2973:
2971:
2967:
2959:
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2949:
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2936:
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2926:
2924:
2921:
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2912:
2906:
2903:
2899:
2896:
2892:
2889:
2887:
2884:
2883:
2882:
2879:
2878:
2877:
2874:
2870:
2867:
2865:
2862:
2860:
2857:
2855:
2852:
2851:
2850:
2847:
2846:
2844:
2842:
2838:
2835:
2833:
2829:
2823:
2820:
2818:
2815:
2811:
2808:
2807:
2806:
2803:
2801:
2798:
2794:
2793:loss function
2791:
2790:
2789:
2786:
2782:
2779:
2777:
2774:
2772:
2769:
2768:
2767:
2764:
2762:
2759:
2757:
2754:
2750:
2747:
2745:
2742:
2740:
2734:
2731:
2730:
2729:
2726:
2722:
2719:
2717:
2714:
2712:
2709:
2708:
2707:
2704:
2700:
2697:
2695:
2692:
2691:
2690:
2687:
2683:
2680:
2679:
2678:
2675:
2671:
2668:
2667:
2666:
2663:
2661:
2658:
2656:
2653:
2651:
2648:
2647:
2645:
2643:
2639:
2635:
2631:
2626:
2622:
2608:
2605:
2603:
2600:
2598:
2595:
2593:
2590:
2589:
2587:
2585:
2581:
2575:
2572:
2570:
2567:
2565:
2562:
2561:
2559:
2555:
2549:
2546:
2544:
2541:
2539:
2536:
2534:
2531:
2529:
2526:
2524:
2521:
2519:
2516:
2515:
2513:
2511:
2507:
2501:
2498:
2496:
2495:Questionnaire
2493:
2491:
2488:
2484:
2481:
2479:
2476:
2475:
2474:
2471:
2470:
2468:
2466:
2462:
2456:
2453:
2451:
2448:
2446:
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2441:
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2433:
2431:
2428:
2426:
2423:
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2418:
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2413:
2409:
2405:
2401:
2396:
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2375:
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2370:
2368:
2365:
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2360:
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2350:
2348:
2345:
2343:
2340:
2338:
2335:
2333:
2330:
2328:
2325:
2323:
2322:Control chart
2320:
2318:
2315:
2313:
2310:
2308:
2305:
2304:
2302:
2300:
2296:
2290:
2287:
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2274:
2273:
2270:
2268:
2265:
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2260:
2259:
2257:
2255:
2251:
2245:
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2240:
2237:
2235:
2232:
2231:
2229:
2225:
2219:
2216:
2215:
2213:
2211:
2207:
2195:
2192:
2190:
2187:
2185:
2182:
2181:
2180:
2177:
2175:
2172:
2171:
2169:
2167:
2163:
2157:
2154:
2152:
2149:
2147:
2144:
2142:
2139:
2137:
2134:
2132:
2129:
2127:
2124:
2123:
2121:
2119:
2115:
2109:
2106:
2104:
2101:
2097:
2094:
2092:
2089:
2087:
2084:
2082:
2079:
2077:
2074:
2072:
2069:
2067:
2064:
2062:
2059:
2057:
2054:
2052:
2049:
2048:
2047:
2044:
2043:
2041:
2039:
2035:
2032:
2030:
2026:
2022:
2018:
2013:
2009:
2003:
2000:
1998:
1995:
1994:
1991:
1987:
1980:
1975:
1973:
1968:
1966:
1961:
1960:
1957:
1945:
1944:
1935:
1933:
1932:
1927:
1923:
1921:
1920:
1911:
1909:
1908:
1899:
1898:
1895:
1889:
1888:
1884:
1882:
1881:
1877:
1875:
1874:
1870:
1868:
1867:
1863:
1861:
1860:
1856:
1855:
1853:
1851:
1846:
1840:
1837:
1835:
1832:
1830:
1827:
1825:
1824:Matrix effect
1822:
1820:
1817:
1815:
1812:
1811:
1809:
1805:
1799:
1796:
1794:
1791:
1789:
1786:
1784:
1783:Pulverization
1781:
1779:
1776:
1774:
1771:
1769:
1766:
1764:
1761:
1759:
1756:
1755:
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1679:
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1654:
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1624:
1619:
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1612:
1610:
1605:
1604:
1601:
1595:
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1583:
1580:
1578:
1575:
1573:
1569:
1566:
1563:
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1555:
1553:
1550:
1549:
1539:
1534:
1530:
1525:
1521:
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1507:
1503:
1498:
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1480:
1476:
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1464:
1459:
1455:
1450:
1446:
1441:
1440:
1428:
1424:
1420:
1416:
1412:
1408:
1401:
1393:
1386:
1378:
1374:
1370:
1366:
1362:
1358:
1354:
1350:
1346:
1342:
1341:
1333:
1325:
1321:
1317:
1313:
1309:
1305:
1301:
1297:
1290:
1282:
1278:
1274:
1270:
1263:
1255:
1251:
1244:
1236:
1232:
1227:
1222:
1218:
1214:
1210:
1203:
1195:
1191:
1187:
1183:
1179:
1175:
1171:
1167:
1163:
1159:
1152:
1144:
1137:
1129:
1123:
1119:
1112:
1104:
1098:
1094:
1087:
1079:
1075:
1071:
1067:
1063:
1059:
1052:
1044:
1040:
1036:
1032:
1028:
1024:
1017:
1009:
1005:
1001:
997:
996:Technometrics
990:
982:
978:
974:
970:
969:Technometrics
963:
955:
951:
947:
943:
938:
933:
929:
925:
921:
917:
913:
909:
902:
894:
890:
886:
882:
878:
874:
870:
866:
859:
851:
845:
841:
834:
826:
822:
818:
814:
813:Technometrics
807:
799:
795:
791:
787:
783:
779:
772:
764:
758:
754:
750:
746:
739:
731:
727:
723:
719:
715:
711:
707:
703:
699:
695:
691:
687:
683:
676:
668:
664:
660:
656:
652:
648:
647:
639:
631:
627:
623:
619:
615:
611:
610:
602:
594:
588:
584:
577:
575:
566:
560:
556:
549:
541:
535:
531:
524:
515:
509:
505:
498:
490:
486:
482:
478:
474:
470:
466:
459:
451:
447:
443:
439:
432:
424:
420:
416:
412:
404:
400:
393:
391:
387:
382:
378:
376:
372:
370:
367:Multivariate
364:
362:
357:
353:
348:
344:
341:
340:
335:
332:
331:
321:
319:
308:
306:
301:
299:
294:
292:
288:
277:
275:
269:
265:
263:
259:
255:
251:
247:
232:
229:
227:
223:
219:
215:
211:
207:
203:
198:
196:
192:
188:
184:
180:
176:
172:
171:
166:
162:
161:
156:
152:
151:
146:
145:
140:
139:
133:
131:
127:
123:
119:
115:
109:
105:
103:
99:
95:
84:
82:
78:
73:
64:
62:
58:
57:psychometrics
54:
50:
46:
42:
38:
34:
30:
26:
21:
4267:
4255:
4236:
4229:
4141:Econometrics
4091: /
4074:Chemometrics
4073:
4051:Epidemiology
4044: /
4017:Applications
3859:ARIMA model
3806:Q-statistic
3755:Stationarity
3651:Multivariate
3594: /
3590: /
3588:Multivariate
3586: /
3526: /
3522: /
3296:Bayes factor
3195:Signed rank
3107:
3081:
3073:
3061:
2756:Completeness
2592:Cohort study
2490:Opinion poll
2425:Missing data
2412:Study design
2367:Scatter plot
2289:Scatter plot
2282:Spearman's Ï
2244:Grouped data
1941:
1929:
1917:
1905:
1885:
1878:
1871:
1864:
1857:
1850:publications
1814:Chemometrics
1813:
1798:Sub-sampling
1737:Spectroscopy
1537:
1528:
1519:
1510:
1501:
1492:
1486:. CRC Press.
1483:
1474:
1462:
1453:
1444:
1410:
1406:
1400:
1391:
1385:
1344:
1338:
1332:
1302:(1): 51â60.
1299:
1295:
1289:
1272:
1268:
1262:
1253:
1249:
1243:
1216:
1212:
1202:
1161:
1157:
1151:
1142:
1136:
1117:
1111:
1095:. Elsevier.
1092:
1086:
1061:
1057:
1051:
1026:
1022:
1016:
999:
995:
989:
972:
968:
962:
937:11567/881059
911:
907:
901:
868:
864:
858:
839:
833:
819:(3): 11â15.
816:
812:
806:
781:
777:
771:
744:
738:
689:
685:
675:
650:
644:
638:
613:
607:
601:
582:
554:
548:
530:Chemometrics
529:
523:
503:
497:
472:
468:
458:
441:
437:
431:
414:
410:
403:
380:
379:
366:
365:
346:
345:
337:
336:
328:
327:
314:
302:
295:
283:
270:
266:
262:mass spectra
243:
230:
222:metabolomics
218:metabonomics
199:
190:
186:
183:Chemometrics
182:
178:
168:
164:
158:
154:
148:
142:
136:
134:
110:
106:
90:
81:metabolomics
74:
70:
61:econometrics
41:biochemistry
20:Chemometrics
19:
18:
4269:WikiProject
4184:Cartography
4146:Jurimetrics
4098:Reliability
3829:Time domain
3808:(LjungâBox)
3730:Time-series
3608:Categorical
3592:Time-series
3584:Categorical
3519:(Bernoulli)
3354:Correlation
3334:Correlation
3130:JarqueâBera
3102:Chi-squared
2864:M-estimator
2817:Asymptotics
2761:Sufficiency
2528:Interaction
2440:Replication
2420:Effect size
2377:Violin plot
2357:Radar chart
2337:Forest plot
2327:Correlogram
2277:Kendall's Ï
1943:WikiProject
1807:Calibration
1768:Dissolution
1707:Calorimetry
1540:. Elsevier.
1522:. Elsevier.
1495:. Elsevier.
258:NMR spectra
246:calibration
94:Svante Wold
4285:Categories
4136:Demography
3854:ARMA model
3659:Regression
3236:(Friedman)
3197:(Wilcoxon)
3135:Normality
3125:Lilliefors
3072:Student's
2948:Resampling
2822:Robustness
2810:divergence
2800:Efficiency
2738:(monotone)
2733:Likelihood
2650:Population
2483:Stratified
2435:Population
2254:Dependence
2210:Count data
2141:Percentile
2118:Dispersion
2051:Arithmetic
1986:Statistics
1848:Prominent
1773:Filtration
1700:Techniques
1681:Microscope
396:References
361:resampling
235:Techniques
214:proteomics
175:Malinowski
126:clustering
122:regression
67:Background
3517:Logistic
3284:posterior
3210:Rank sum
2958:Jackknife
2953:Bootstrap
2771:Bootstrap
2706:Parameter
2655:Statistic
2450:Statistic
2362:Run chart
2347:Pie chart
2342:Histogram
2332:Fan chart
2307:Bar chart
2189:L-moments
2076:Geometric
1742:Titration
1324:120516715
730:249129065
714:0003-7028
667:221546473
630:120490459
489:123071521
475:: 53â64.
386:data cube
37:chemistry
4231:Category
3924:Survival
3801:Johansen
3524:Binomial
3479:Isotonic
3066:(normal)
2711:location
2518:Blocking
2473:Sampling
2352:QâQ plot
2317:Box plot
2299:Graphics
2194:Skewness
2184:Kurtosis
2156:Variance
2086:Heronian
2081:Harmonic
1907:Category
1763:Dilution
1751:Sampling
1590:Archived
1568:Archived
1513:. Wiley.
1456:. Wiley.
1447:. Wiley.
1394:. Wiley.
1377:38093353
1369:17749872
1235:50546210
1194:73727614
1186:30851858
1164:: 9â17.
1078:95309963
954:10119515
946:28734370
914:: 9â19.
893:21166415
885:11228707
798:15283574
722:35622984
293:scores.
250:infrared
210:genomics
45:medicine
4296:Metrics
4257:Commons
4204:Kriging
4089:Process
4046:studies
3905:Wavelet
3738:General
2905:Plug-in
2699:L space
2478:Cluster
2179:Moments
1997:Outline
1919:Commons
1859:Analyst
1778:Masking
1415:Bibcode
1349:Bibcode
1340:Science
1304:Bibcode
1256:: 8â10.
1166:Bibcode
1031:Bibcode
916:Bibcode
694:Bibcode
390:PARAFAC
170:Talanta
116:(PCA),
87:Origins
49:biology
4126:Census
3716:Normal
3664:Manova
3484:Robust
3234:2-way
3226:1-way
3064:-test
2735:
2312:Biplot
2103:Median
2096:Lehmer
2038:Center
1931:Portal
1375:
1367:
1322:
1233:
1192:
1184:
1124:
1099:
1076:
952:
944:
891:
883:
846:
796:
759:
728:
720:
712:
665:
628:
589:
561:
536:
510:
487:
371:(MSPC)
189:, and
147:, and
128:, and
31:, and
3750:Trend
3279:prior
3221:anova
3110:-test
3084:-test
3076:-test
2983:Power
2928:Pivot
2721:shape
2716:scale
2166:Shape
2146:Range
2091:Heinz
2066:Cubic
2002:Index
1557:IUPAC
1373:S2CID
1320:S2CID
1231:S2CID
1190:S2CID
1074:S2CID
950:S2CID
889:S2CID
726:S2CID
663:S2CID
626:S2CID
485:S2CID
274:LC-MS
254:Raman
3983:Test
3183:Sign
3035:Wald
2108:Mode
2046:Mean
1365:PMID
1182:PMID
1162:1058
1122:ISBN
1097:ISBN
942:PMID
881:PMID
844:ISBN
794:PMID
757:ISBN
718:PMID
710:ISSN
587:ISBN
559:ISBN
534:ISBN
508:ISBN
260:and
220:and
202:QSAR
195:Naes
79:and
59:and
51:and
3163:BIC
3158:AIC
1423:doi
1357:doi
1345:226
1312:doi
1277:doi
1221:doi
1174:doi
1066:doi
1039:doi
1027:500
1004:doi
977:doi
932:hdl
924:doi
912:982
873:doi
869:368
821:doi
786:doi
749:doi
702:doi
655:doi
618:doi
477:doi
446:doi
419:doi
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