Test for High-Dimensional Data Under Sparsity

• Activity Number: 476
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Ping-Shou Zhong*+ and Ping-Shou Zhong
• Companies: Iowa State University and Iowa State University
• Keywords: High dimensional data ; Large p, small n ; Sparsity

Abstract

In this study, we consider detecting sparse signal in the high dimensional but small sample size data. We propose a threshold test statistic for simultaneous tests on the high dimensional mean under the sparsity condition. The asymptotic distributions of the test statistic are derived for the non-normal and dependent data under the "large p, small n" scenarios. We show that the proposed test could achieve the optimal detection boundary under weak dependence assumption. It was also found that the proposed test performs better than the high dimensional test proposed by Chen and Qin (2010) under the sparsity condition.