Homogeneity Test of Multi-Sample Covariance Matrices in High Dimensions

Abstract

In this paper, a new test statistic based on the weighted Frobenius norm of covariance matrices is proposed to test the homogeneity of multi-group population covariance matrices. The asymptotic distributions of the proposed test under the null and the alternative hypotheses are derived, respectively. Simulation results show that the proposed test procedure tends to outperform some existing test procedures.

Keywords

• high-dimensional data
• weighted Frobenius norm
• homogeneity test
• martingale central limit theorem
• asymptotic distributions