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

In this article, we propose an L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document}-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.