In this paper, we propose a new modified likelihood ratio test (LRT) for simultaneously testing mean vectors and covariance matrices of two-sample populations in high-dimensional settings. By employing tools from Random Matrix Theory (RMT), we derive the limiting null distribution of the modified LRT for generally distributed populations. Furthermore, we compare the proposed test with existing tests using simulation results, demonstrating that the modified LRT exhibits favorable properties in terms of both size and power.

翻译：本文针对高维情形下两个样本总体的均值向量和协方差矩阵，提出了一种新的修正似然比检验方法。利用随机矩阵理论工具，推导了一般分布总体下修正似然比检验的渐近零分布。此外，通过模拟研究将所提检验与现有检验进行对比，结果表明修正LRT在检验水平和检验功效方面均表现出良好性质。