Finite skew-mixture models for estimation of positive false discovery rates

We propose a mixture model framework for estimating positive false discovery rates in multiple-testing problems. The density of a transformed pp-value is modeled by a finite mixture of skewed distributions. We argue that a mixture of skewed distributions like the skew-normal one is better for addressing some features in modeling than the more commonly used mixture of normal distributions. Using the fitted distributions, we estimate the proportion of true null hypotheses, the positive false discovery rate and other important functionals in multiple-testing problems. We investigate the performance of our methodology via simulation and illustrate the effectiveness of the proposed procedure using real data examples. We also discuss the role of an empirical null in place of the theoretical null distributions in the context of common biomedical applications.