Multiple Testing Using Nonparametric and Semiparametric Models

• Activity Number: 45
• Type: Other
• Date/Time: Sunday, August 1, 2010 : 4:00 PM to 5:50 PM
• Sponsor: ASA
• Author(s): Peter H. Westfall*+
• Companies: Texas Tech University

Abstract

An overview of multiple testing is given for nonparametric or semi-parametric models. Nonparametric permutation-based methods are described that have precise finite sample control of Type I errors under very minimal assumptions; many applications are given. The methods are surprisingly powerful despite minimal assumptions; in some cases they are more powerful than normal-theory counterparts. The explanation lies in the way that discreteness of the sampling distributions is incorporated. These nonparametric methods can be made even more powerful by incorporating dependence structure via vector permutation, at the expense of further assumptions. Bootstrap methods are also discussed for semi-parametric models; these methods can incorporate dependence structures with somewhat less restrictive assumptions, but occasionally lose finite-sample type I error control.