Simultaneous testing of the mean vector and covariance matrix among k populations for high-dimensional data

In this study, we propose an L-2-norm-based test for simultaneous testing of the mean vector and covariance matrix for high-dimensional non-normal populations. We extend to k sample problems the procedures developed for two-sample problems by Hyodo and Nishiyama [Hyodo, M., Nishiyama, T., A simultaneous testing of the mean vector and the covariance matrix among two populations for high-dimensional data, TEST]. To accomplish this, we derive an asymptotic distribution of a test statistic based on differences of both mean vectors and covariance matrices. We also investigate the asymptotic sizes and powers of the proposed tests using this result. Finally, we study the finite sample and dimension performance of this test through Monte Carlo simulations.