Two-Sample Test for High-Dimensional Covariance Matrices

• Activity Number: 311
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Jing He* and Song Xi Chen
• Companies: Peking University and Peking University/Iowa State Univeristy
• Keywords: High Dimensionality ; Large $p$ Small $n$ ; Sparse Covariance Matrix ; Multiple Testing

Abstract

Testing the equality of two covariance matrices plays an important part in discovering significant differences between two high-dimensional distributions. We consider a more powerful two sample test procedure which focuses on testing along the super-diagonals of the high dimensional covariance matrices. We show that the proposed test has less variability and attains larger signal to noise ratio and hence an increase in the power. Our test allows the dimension to be much larger than the sample size and does not require assumptions on the distribution of the two populations. The properties of the test are demonstrated by theoretical analyses, and simulation and empirical studies.