title: Testing multiple hypotheses with skewed alternatives.
abstract: In many practical cases of multiple hypothesis problems, it can be expected that the alternatives are not symmetrically distributed. If it is known a priori that the distributions of the alternatives are skewed, we show that this information yields high power procedures as compared to the procedures based on symmetric alternatives when testing multiple hypotheses. We propose a Bayesian decision theoretic rule for multiple directional hypothesis testing, when the alternatives are distributed as skewed, under a constraint on a mixed directional false discovery rate. We compare the proposed rule with a frequentist's rule of Benjamini and Yekutieli (2005) using simulations. We apply our method to a well-studied HIV dataset.
authors.affiliation: Department of Mathematics, Statistics, and Computer Sciences, Marquette University, Milwaukee, Wisconsin 53201-1881, U.S.A.
authors.forename: Naveen K
authors.initials: NK
authors.lastname: Bansal
authors.affiliation: Department of Mathematics, Statistics, and Computer Sciences, Marquette University, Milwaukee, Wisconsin 53201-1881, U.S.A.
authors.forename: Gholamhossein G
authors.initials: GG
authors.lastname: Hamedani
authors.affiliation: Department of Mathematics, Statistics, and Computer Sciences, Marquette University, Milwaukee, Wisconsin 53201-1881, U.S.A.
authors.forename: Mehdi
authors.initials: M
authors.lastname: Maadooliat
mesh_terms: D016477:Artifacts; D001499:Bayes Theorem; D019295:Computational Biology / Q000706:statistics & numerical data*; D003198:Computer Simulation; D020869:Gene Expression Profiling; D015658:HIV Infections / Q000235:genetics; D006801:Humans; D015233:Models, Statistical; D009010:Monte Carlo Method; D020411:Oligonucleotide Array Sequence Analysis
keywords: Bayes rule; Directional hypotheses; False discovery rate; Gene expressions; Skew normal distribution