title: Compoundp-value statistics for multiple testing procedures.
abstract: Many multiple testing procedures make use of thep-values from the individual pairs of hypothesis tests, and are valid if thep-value statistics are independent and uniformly distributed under the null hypotheses. However, it has recently been shown that these types of multiple testing procedures are inefficient since suchp-values do not depend upon all of the available data. This paper provides tools for constructingcompound p-value statistics, which are those that depend upon all of the available data, but still satisfy the conditions of independence and uniformity under the null hypotheses. Several examples are provided, including a class of compoundp-value statistics for testing location shifts. It is demonstrated, both analytically and through simulations, that multiple testing procedures tend to reject more false null hypotheses when applied to these compoundp-values rather than the usualp-values, and at the same time still guarantee the desired type I error rate control. The compoundp-values are used to analyze a real microarray data set and allow for more rejected null hypotheses.
authors: Department of Statistics, Oklahoma State University, 301 MSCS building, Stillwater, OK, 74078, United States.
authors: Joshua D
authors: JD
authors: Habiger
authors: Department of Statistics, University of South Carolina, 216 LeConte College, Columbia, SC, 29208, United States.
authors: Edsel A
authors: EA
authors: Peña
keywords: Empirical Bayes; False discovery rate; Microarray analysis; Multiple decision function; Multiple decision process; Multiple testing; Sample splitting; Test data; Training data