Optimal Multiple Testing Procedure Under Linear Regression Model

• Activity Number: 407
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Zhigen Zhao*+ and Jichun Xie
• Companies: Temple University and Temple University
• Keywords: Multiple testing ; regresion ; FDR ; optimal

Abstract

In this paper, we construct an multiple testing procedure for the linear regression model Y=X beta+epsilon when the dimension p is much larger than the sample size n. Such a model is a generalization of the multiple testing for a normal mean problem with an arbitrary dependence structure.

To the best of the authors' knowledge, this is the first multiple testing procedure which controls the FDR at any designated alpha-level for the regression model. Since we need to use the sure independence screening (SIS), the conditions required for the design matrix X is the necessary condition for the SURE property (Fan and Lv,2008). The design matrix X can be chosen almost arbitrarily. In addition, the current method minimizes the FNR among all the testing procedures which control the FDR at the specified level.

We also use the simulation studies and real data analysis to compare the current methods with its alternatives, including BH procedure and many others. Please come and see how it works.