A Test For The Equality Of Two Large-dimensional Covariance Matrices

This paper is mainly about the test of the equality of large-dimensional covariance matrices from two different populations. The equality of covariance matrices is the simplest form of heteroscedasticity between populations, which has extensive applications in economics, discriminations, etc. But when we deal with the large dimensional data, most of the traditional multiple statistics are no more valid or perform badly. We should improve and use new method to deal with the problems of large dimensional data. In the second chapter of this article, we propose a new statistic for the covariance matrices test. Based on the central limit theorems for linear spectral statistics of large dimensional F-matrices, this paper proves asymptotic normality property as the dimension p and sample size(1, 2) tend to infinity. The new statistic is compared with the test proposed by Li and Chen(2012)[3]. And in the third chapter of the paper some simulation studies show that the new test statistic behaves well.