高维协方差阵的两样本检验的一些证明

Some Proofs on Two Sample Tests for High Dimensional Covariance Matrices

假定样本总体的维数为p,样本容量为n,当p<n时,单个及多个p元正态总体的协方差阵的检验问题已经解决,但是当p比n大很多时,我们发现已有的解决方法失效,参见文献[3-4].文献[1]提出了一般条件下两样本协方差阵检验的检验统计量,本文将为这个统计量的渐近正态性的相关结论给出证明.

We suppose that the dimension of population is p and the sample size is n. When p〈n ,the tests for the variance-covariance matrices of one and multi p dimensional normal populations are solved; When p is much larger than n, the methods in [3-4] isn＇ t work. The test statistic of the two-sample test for the whole covariance matrices was proposed in literatrue Ill. In this article, we will proof some results on the normality of this test statistic.