This paper proposes new classifiers under the assumption of multivariate normality for multivariate repeated measures data (doubly multivariate data) with Kronecker product covariance structures. These classifiers are especially useful when the number of observations is not large enough to estimate the covariance matrices, and thus the traditional classifiers fail. The quality of these new classifiers is examined on some real data. Computational schemes for maximum likelihood estimates of required class parameters, and the likelihood ratio test relating to the structure of the covariance matrices, are also given.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1135,
author = {Miros\l aw Krzy\'sko and Micha\l\ Skorzybut and Waldemar Wo\l y\'nski},
title = {Classifiers for doubly multivariate data},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {31},
year = {2011},
pages = {5-27},
zbl = {1260.62044},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1135}
}
Mirosław Krzyśko; Michał Skorzybut; Waldemar Wołyński. Classifiers for doubly multivariate data. Discussiones Mathematicae Probability and Statistics, Tome 31 (2011) pp. 5-27. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1135/
[000] [1] K.M. Abadir and J.R. Magnus, Matrix Algebra (Cambridge University Press, New York, 2005). doi: 10.1017/CBO9780511810800. | Zbl 1084.15001
[001] [2] A.T. Galecki, General class of covariance structures for two or more repeated factors in longitudinal data analysis, Communications in Statistics - Theory and Methods 23 (1994) 3105-3119. doi: 10.1080/03610929408831436. | Zbl 0875.62274
[002] [3] N.C. Giri, Multivariate Statistical Analysis (Marcel Dekker, Inc., New York, 1996). | Zbl 0846.62039
[003] [4] D.N. Naik and S. Rao, Analysis of multivariate repeated measures data with a Kronecker product structured covariance matrix, J. Appl. Statist. 28 (2001) 91-105. doi: 10.1080/02664760120011626. | Zbl 0991.62038
[004] [5] A. Roy and R. Khattree, Discrimination and classification with repeated measures data under different covariance structures, Communications in Statistics - Simulation and Computation 34 (2005a) 167-178. doi: 10.1081/SAC-200047072. | Zbl 1061.62090
[005] [6] A. Roy and R. Khattree, On discrimination and classification with multivariate repeated measures data, Journal of Statistical Planning and Inference 134 (2005b) 462-485. doi: 10.1016/j.jspi.2004.04.012. | Zbl 1066.62069
[006] [7] A. Roy and R. Khattree, Classification rules for repeated measures data from biomedical research, in: Computational methods in biomedical research, R. Khattree, D.N. Naik (Ed(s)), (Chapman and Hall/CRC, 2008) 323-370.
[007] [8] SAS Institute Inc., SAS procedures guide, Version 6, Third Edition (Cary, NC: SAS Institute Inc, 1990).
[008] [9] G.A.F. Seber, Multivariate Observations (Wiley, New York, 1984). doi: 10.1002/9780470316641. | Zbl 0627.62052
[009] [10] S.M. Srivastava, T. von Rosen and D. von Rosen, Models with a Kronecker product covariance structure: estimation and testing, Math. Methods Stat. 17(4) (2008) 357-370. doi: 10.3103/S1066530708040066. | Zbl 1231.62101
[010] [11] A. Wald, Tests of statistical hypotheses concerning several parameters when the number of observations is large, Transactions of the American Mathematical Society 54 (1943) 426-483. doi: 10.1090/S0002-9947-1943-0012401-3. | Zbl 0063.08120