Testing homogeneity of several covariance matrices and multi-sample sphericity for high-dimensional data under non-normality

A test for homogeneity of g ⩾ 2 covariance matrices is presented when the dimension, p, may exceed the sample size, n i , i = 1, ..., g, and the populations may not be normal. Under some mild assumptions on covariance matrices, the asymptotic distribution of the test is shown to be normal when n i ,...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2017-04, Vol.46 (8), p.3738-3753
Main Author: Ahmad, M. Rauf
Format: Article
Language:English
Subjects:
62H15
Covariance
High-dimensionality
Homogeneity
multi-sample sphericity
non-normality
Null hypothesis
Samples
Shape
Simulation
Statistical methods
Statistics
U-statistics
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Summary:A test for homogeneity of g ⩾ 2 covariance matrices is presented when the dimension, p, may exceed the sample size, n i , i = 1, ..., g, and the populations may not be normal. Under some mild assumptions on covariance matrices, the asymptotic distribution of the test is shown to be normal when n i , p → ∞. Under the null hypothesis, the test is extended for common covariance matrix to be of a specified structure, including sphericity. Theory of U-statistics is employed in constructing the tests and deriving their limits. Simulations are used to show the accuracy of tests.
ISSN:0361-0926
1532-415X
1532-415X
DOI:10.1080/03610926.2015.1073310