Abstract: This paper considers testing for two-sample covariance matrices of high-dimensional populations. We formulate a multiple test procedure by comparing the super-diagonals of the covariance matrices. The asymptotic distributions of the test statistics are derived and the powers of individual tests are studied. The test statistics, by focusing on the super-diagonals, have smaller variation than the existing tests that target on the entire covariance matrix. The advantage of the proposed test is demonstrated by simulation studies, as well as an empirical study on a prostate cancer dataset.

Key words and phrases: High dimensional test, multiple test, sparse alternative, two-sample test for covariance matrices.