Simultaneous testing of mean vector and covariance matrix for high-dimensional data

•Testing mean vector and covariance matrix for high dimensional data simultaneously.•Establishing a central limit theorem of the proposed test statistic.•Requiring only that the fourth population moment exists.

A new method is proposed to simultaneously test mean vector and covariance matrix for high-dimensional data. It allows for the case of large dimension p and small sample size n, and it is also robust against non-Gaussian data. Besides, the asymptotic null distribution is derived and the asymptotic theoretical power function is explicitly achieved. The local power of the new method is studied and the proposed test is proved to be asymptotically unbiased. Finally, the efficiency of the new method is assessed by numerical simulations.