Physical Sciences and Mathematics Commons^™

Multiple Testing. Part I. Single-Step Procedures For Control Of General Type I Error Rates, Sandrine Dudoit, Mark J. Van Der Laan, Katherine S. Pollard

U.C. Berkeley Division of Biostatistics Working Paper Series

The present article proposes general single-step multiple testing procedures for controlling Type I error rates defined as arbitrary parameters of the distribution of the number of Type I errors, such as the generalized family-wise error rate. A key feature of our approach is the test statistics null distribution (rather than data generating null distribution) used to derive cut-offs (i.e., rejection regions) for these test statistics and the resulting adjusted p-values. For general null hypotheses, corresponding to submodels for the data generating distribution, we identify an asymptotic domination condition for a null distribution under which single-step common-quantile and common-cut-off procedures asymptotically …