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.
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Acknowledgments
Sincere thanks to the editor, the associate editor and two anonymous referees whose comments helped significantly improve the paper.