False Discovery Rate for Infinitely Many Comparisons

• Activity Number: 341
• Type: Invited
• Date/Time: Wednesday, August 10, 2005 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Peter Westfall*+
• Companies: Texas Tech University

Abstract

Connections between Benjamini and Hochberg's FDR-controlling procedure and the Waller-Duncan k-ratio method have been noted by Shaffer (1999) and Lewis and Thayer (2005). This connection is clarified by obtaining and studying exact and approximate critical points for the FDR method when used to test infinitely many contrasts in linear models and by noting their similarity with the Waller-Duncan k-ratio critical points. Exact limiting critical points are obtained under the assumption the contrasts are randomly selected from the unit sphere embedded in contrast space, and it is shown that the resulting exact FDR critical points depend on the data only through the F statistic. Similar results are obtained for general correlation structures, but require a suitable redefinition of a "randomly sampled contrast." In this paper, this new method for testing contrasts in linear models is developed and compared with existing methods analytically. All results are nonparametric in the sense that no distributional assumptions are made; yet, interestingly, the critical points are shown to be functions of the usual t and F distributions.