Testing the equality of several covariance matrices with fewer observations than the dimension

Authors:
Muni S. Srivastava;Hirokazu Yanagihara
Affiliations:
Department of Statistics, University of Toronto, 100 St George Street, Toronto, Ontario, M5S 3G3, Canada;Department of Mathematics, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8626, Japan
Venue:
Journal of Multivariate Analysis
Year:
2010

Citing 2
Cited 2

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A test for the equality of covariance matrices when the dimension is large relative to the sample sizes

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Testing the structure of the covariance matrix with fewer observations than the dimension

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A two sample test in high dimensional data

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Abstract

For normally distributed data from the k populations with mxm covariance matrices @S"1,...,@S"k, we test the hypothesis H:@S"1=...=@S"k vs the alternative AH when the number of observations N"i, i=1,...,k from each population are less than or equal to the dimension m, N"i@?m, i=1,...,k. Two tests are proposed and compared with two other tests proposed in the literature. These tests, however, do not require that N"i@?m, and thus can be used in all situations, including when the likelihood ratio test is available. The asymptotic distributions of the test statistics are given, and the power compared by simulations with other test statistics proposed in the literature. The proposed tests perform well and better in several cases than the other two tests available in the literature.