A False Important Discovery Approach to Testing Large Non-Null Effects

• Activity Number: 649
• Type: Invited
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Wenguang Sun*+ and Alexander McLain
• Companies: North Carolina State University and National Institutes of Health
• Keywords: Compound decision problem ; deconvoluting kernel density estimator ; exchangeability of hypotheses ; false important discovery rate ; large-scale multiple testing

Abstract

In large-scale studies, the true effect sizes often range continuously from zero to small to large. We discuss some philosophical issues regarding the proper formulation of a multiple testing problem and develop a new false important discovery approach to testing large non-null effects. We demonstrate that the common strategy in multiple testing for testing non-zero effects is inappropriate because the data summarization step may totally distort the scientific question and lead to misleading conclusions. Our approach is different from conventional procedures in that both the statistical significance and effect size problems are addressed simultaneously. The asymptotic validity and asymptotic optimality of our data-driven procedure are established in compound decision-theoretic framework. The advantages of the new testing procedure are demonstrated using both simulated and real data.