Hypothesis Testing for Large Dimensional Covariance Matrices

• Activity Number: 85
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Yingli Qin*+ and Weiming Li
• Companies: University of Waterloo and Beijing University of Posts and Telecommunications
• Keywords: hypothesis testing ; high-dimensional ; covariance matrix ; random matrix theory ; Stieltjes transform ; asymptotic

Abstract

In this paper, we propose statistics for testing whether a covariance matrix is an identify matrix and the equality of two covariance matrices in high-dimensional framework. The proposed test statistics are based on the Stieltjes transform of the spectral distribution of the sample covariance matrix. Through Random Matrix Theory, we prove that the proposed test statistics are asymptotically generalized chi-square distributed under null hypotheses. Simulation results are presented to show that the proposed tests outperform some existing methods in various cases.