Estimating False Discovery Proportion Under Arbitrary Dependance

• Activity Number: 150
• Type: Invited
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: JASA, Theory and Methods
• Author(s): Jianqing Fan*+ and Xu Han and Weijie Gu
• Companies: Princeton University and University of Florida and Princeton University
• Keywords: FDR ; Principle component analysis ; dependence ; factor adjustment ; sparsity

Abstract

Multiple hypothesis testing is a fundamental problem in high dimensional inference. When test statistics are correlated, false discovery control becomes very challenging under arbitrary dependence. In the current paper, we propose a novel method based on principal factor approximation, which successfully subtracts the common dependence and weakens significantly the correlation structure, to deal with an arbitrary dependence structure. We derive an approximate expression for false discovery proportion (FDP) in large scale multiple testing when a common threshold is used and provide a consistent estimate of realized FDP. This result has important applications in controlling FDR and FDP. Our estimate of realized FDP compares favorably with Efron (2007)'s approach, as demonstrated in the simulated examples. Our approach is further illustrated by some real data applications. We also propose a dependence-adjusted procedure, which is more powerful than the fixed threshold procedure.