A Two-Sample Test for High-Dimensional Covariance Matrices via Sparse Principal Component Analysis

• Activity Number: 185
• Type: Contributed
• Date/Time: Monday, August 1, 2016 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Lingxue Zhu* and Jing Lei and Bernie Devlin and Kathryn Roeder
• Companies: Carnegie Mellon University and Carnegie Mellon University and University of Pittsburgh School of Medicine and Carnegie Mellon University
• Keywords: hypothesis testing ; covariance matrix ; sparse principal component analysis ; high-dimensional data

Abstract

We propose a permutation test for two-sample covariance matrices under the high-dimensional setting. Our test provides a novel perspective that evaluates the spectrum of the difference between two covariance matrices. The test statistic is closely related with Sparse Principal Component Analysis and accommodates the sparse and weak signals in many gene expression data. Our test achieves full power asymptotically under mild conditions, and simulation studies verify that it outperforms other existing procedures for many biologically plausible settings. Applying our method to a gene-expression dataset comparing Schizophrenia and control brains, we reveal intriguing patterns of gene co-expression change between two groups of subjects.