# Classifiers for doubly multivariate data

Mirosław Krzyśko; Michał Skorzybut; Waldemar Wołyński

Discussiones Mathematicae Probability and Statistics (2011)

- Volume: 31, Issue: 1-2, page 5-27
- ISSN: 1509-9423

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topMirosław Krzyśko, Michał Skorzybut, and Waldemar Wołyński. "Classifiers for doubly multivariate data." Discussiones Mathematicae Probability and Statistics 31.1-2 (2011): 5-27. <http://eudml.org/doc/277033>.

@article{MirosławKrzyśko2011,

abstract = {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.},

author = {Mirosław Krzyśko, Michał Skorzybut, Waldemar Wołyński},

journal = {Discussiones Mathematicae Probability and Statistics},

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; repeated measures data; Kronecker product; covariance structure},

language = {eng},

number = {1-2},

pages = {5-27},

title = {Classifiers for doubly multivariate data},

url = {http://eudml.org/doc/277033},

volume = {31},

year = {2011},

}

TY - JOUR

AU - Mirosław Krzyśko

AU - Michał Skorzybut

AU - Waldemar Wołyński

TI - Classifiers for doubly multivariate data

JO - Discussiones Mathematicae Probability and Statistics

PY - 2011

VL - 31

IS - 1-2

SP - 5

EP - 27

AB - 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.

LA - eng

KW - 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; repeated measures data; Kronecker product; covariance structure

UR - http://eudml.org/doc/277033

ER -

## References

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- [8] SAS Institute Inc., SAS procedures guide, Version 6, Third Edition (Cary, NC: SAS Institute Inc, 1990).
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- [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. Zbl1231.62101
- [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. Zbl0063.08120

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