In this article, we propose an L 2 -norm-based test for simultaneous testing
of the mean vector and the covariance matrix under high-dimensional non-normal
populations. To construct this, we derive an asymptotic distribution of a test statistic
based on both differences mean vectors and covariance matrices. We also investigate
the asymptotic sizes and powers of the proposed test using this result. Finally, we study
the finite sample and dimension performance of this test via Monte Carlo simulations.

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• A simultaneous testing of the mean vector and the covariance matrix among two populations for high-dimensional data