Testing homogeneity of several covariance matrices and multi-sample sphericity for high-dimensional data under non-normality |
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Authors: | M Rauf Ahmad |
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Institution: | Department of Statistics, Uppsala University, Uppsala, Sweden |
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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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Keywords: | High-dimensionality multi-sample sphericity non-normality U-statistics |
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