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Title: Simultaneous test for mean vectors and covariance matrices among k populations for high-dimensional data Authors:  Takahiro Nishiyama - Senshu University (Japan) [presenting]
Hayate Ogawa - Osaka prefecture university (Japan)
Masashi Hyodo - Osaka Prefecture University (Japan)
Abstract: A simultaneous test for mean vectors and covariance matrices among $k$ populations in non-normal high-dimensional data is proposed. Since the classical hypothesis testing methods based on the likelihood ratio degenerate when the dimensionality exceeds the sample size, we propose a new $L^2$-norm-based test. To construct a test procedure, we propose a test statistic based on both an unbiased estimator of differences of mean vectors and covariance matrices. Also, we derive an asymptotic null distribution of this test statistic. Finally, we study the finite sample and dimension performance of this test via Monte Carlo simulations. We demonstrate the relevance and benefits of the proposed approach for some alternative mean and covariance structures.