A Comparative Study of Two-Sample Tests for High-Dimensional Covariance Matrices

The equality of covariance matrices is an essential assumption in means and discriminant analyses for high-dimensional data. The performance of tests for covariance matrices may vary substantially depending on the covariance structure, so using inappropriate methods to verify the assumption will result in worse performance. The purpose of this study is to assess and compare the performance of three tests for two-sample high-dimensional covariance matrices: Schott’s (2007), Srivastava and Yanagihara’s (2010), and Li and Chen’s (2012) under various covariance structures. A simulation study was conducted when the covariance structures were spherical, compound symmetric, block-diagonal, and first-order autoregressive with homogenous variances. The results show that Li and Chen’s test outperforms the others with a sample size of at least 10 under particular covariance structures. When the number of variables is increased with a fixed sample size, Li and Chen’s test still performs well, whereas Schott’s performance deteriorates. Some recommendations for selecting appropriate tests are also provided in this paper.