A Test For The Equality Of Two High-Dimensional Covariance Matrices

In modern statistical analysis, high dimensional data is often encountered. And the conventional statistical inference method can no longer be used in this situation for the data dimension is much larger than the sample size, namely the situation of "large p, small n"In this paper, a new statistic is proposed for testing the equality of covariance matrices of two populations, no matter what kind of populations they are, in the situation of "large p, small n". Especially, the test is well fit for the situation in which p is substantially larger than n. Both theoretical and empirical studies are carried out to prove the test have good properties in a variety of situations.The assumptions for the proposed test are easily reached in the case of high dimension. What’s more, the proposed test can be used in non-normal case which gives its application a lot of convenience, for the already raised test for testing the covariance matrices of two high dimensional populations mainly focus on normal populations.