On LR simultaneous test of high-dimensional mean vector and covariance matrix under non-normality

Abstract

In this paper, we primarily focus on simultaneous testing mean vector and covariance matrix with high-dimensional non-Gaussian data, based on the classical likelihood ratio test. Applying the central limit theorem for linear spectral statistics of sample covariance matrices, we establish new modification for the likelihood ratio test, and find that this modified test converges in distribution to normal distribution, when the dimension p tends to infinity, proportionate to the sample size n under the null hypothesis. Furthermore, we conduct a simulation study to examine the performance of the test and compare it with other tests proposed in past studies. As the simulation results show, our empirical powers are clearly superior to those of other tests in a series of settings.