Rate Optimal Multiple Testing Procedure in High-Dimensional Regression

• Activity Number: 290
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Zhigen Zhao*+ and Pengsheng Ji
• Companies: Temple University and University of Georgia
• Keywords: oracle ; optimal ; convergence rate ; FDR ; FNR ; loss function

Abstract

Multiple testing and variable selection have gained much attention in statistical theory and methodology research. They are dealing with the same problem--identifying the important variables among many. However, there is little overlap in the literature. Research on variable selection has been focusing on selection consistency, i.e., both type I and type II errors converge to zero. This is only possible when the signals are sufficiently strong, contrary to many modern applications. For raw and rare signals, it is thus inevitable to allow a certain amount of false discoveries, as long as some error rate can be controlled. In this paper, we propose a two-stage testing procedure, named as the TT method. We show that the TT method achieves the fastest convergence rate of marginal false non-discovery rate while controlling the marginal false discovery rate at any designated level $\alpha$ asymptotically under certain conditions. Numerical results are provided to demonstrate the advantage of the proposed method.