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

M. Rauf Ahmad

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 8, 3738-3753

Abstract: A test for homogeneity of g ⩾ 2 covariance matrices is presented when the dimension, p, may exceed the sample size, ni, 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 ni, 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.

Date: 2017
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DOI: 10.1080/03610926.2015.1073310

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