Geodesic
Classifiers for doubly multivariate data
Discussiones Mathematicae. Probability and Statistics, Tome 31 (2011) no. 1-2, pp. 5-27.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: classifiers, repeated measures data (doubly multivariate data), Kronecker product covariance structure, compound symmetry covariance structure, AR(1) covariance structure, maximum likelihood estimates, likelihood ratio tests 
@article{DMPS_2011_31_1-2_a0,
     author = {Krzy\'sko, Miros{\l}aw and Skorzybut, Micha{\l} and Wo{\l}y\'nski, Waldemar},
     title = {Classifiers for doubly multivariate data},
     journal = {Discussiones Mathematicae. Probability and Statistics},
     pages = {5--27},
     publisher = {mathdoc},
     volume = {31},
     number = {1-2},
     year = {2011},
     zbl = {1260.62044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMPS_2011_31_1-2_a0/}
}
TY  - JOUR
AU  - Krzyśko, Mirosław
AU  - Skorzybut, Michał
AU  - Wołyński, Waldemar
TI  - Classifiers for doubly multivariate data
JO  - Discussiones Mathematicae. Probability and Statistics
PY  - 2011
SP  - 5
EP  - 27
VL  - 31
IS  - 1-2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMPS_2011_31_1-2_a0/
LA  - en
ID  - DMPS_2011_31_1-2_a0
ER  - 
%0 Journal Article
%A Krzyśko, Mirosław
%A Skorzybut, Michał
%A Wołyński, Waldemar
%T Classifiers for doubly multivariate data
%J Discussiones Mathematicae. Probability and Statistics
%D 2011
%P 5-27
%V 31
%N 1-2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMPS_2011_31_1-2_a0/
%G en
%F DMPS_2011_31_1-2_a0
Krzyśko, Mirosław; Skorzybut, Michał; Wołyński, Waldemar. Classifiers for doubly multivariate data. Discussiones Mathematicae. Probability and Statistics, Tome 31 (2011) no. 1-2, pp. 5-27. http://geodesic.mathdoc.fr/item/DMPS_2011_31_1-2_a0/

[1] K.M. Abadir and J.R. Magnus, Matrix Algebra (Cambridge University Press, New York, 2005). doi: 10.1017/CBO9780511810800.

[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.

[3] N.C. Giri, Multivariate Statistical Analysis (Marcel Dekker, Inc., New York, 1996).

[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.

[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.

[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.

[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.

[8] SAS Institute Inc., SAS procedures guide, Version 6, Third Edition (Cary, NC: SAS Institute Inc, 1990).

[9] G.A.F. Seber, Multivariate Observations (Wiley, New York, 1984). doi: 10.1002/9780470316641.

[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.

[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.