Multiple Testing for Sparse Covariance Matrices

• Activity Number: 290
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Jing He*+ and Song Xi Chen
• Companies: Peking University and Iowa State University/Peking University
• Keywords: High Dimension ; Asymptotic Normality ; Sparse Covariance ; Multiple testing

Abstract

Testing covariance structure has drawn increasing attention in many areas of statistical analysis. Motivated by the widespread applications, we propose in this paper a multiple test procedure for certain sub-diagonals of high-dimensional sparse covariance matrices. This test procedure is facilitated after establishing the asymptotic normality of test statistics along the sub-diagonals. This test can also be used to test the bandedness of a high-dimensional covariance matrix. We show that the test is powerful in detecting sparse signals in the covariance. The properties of the test are demonstrated by both theoretical and simulation studies.