Multiple Testing under Dependence via Semiparametric Graphical Models

Abstract

It has been shown that graphical models can be used to leverage the dependence in large-scale multiple testing problems with significantly improved performance (Sun & Cai, 2009; Liu et al., 2012). These graphical models are fully parametric and require that we know the parameterization of f1 — the density function of the test statistic under the alternative hypothesis. However in practice, f1 is often heterogeneous, and cannot be estimated with a simple parametric distribution. We propose a novel semiparametric approach for multiple testing under dependence, which estimates f1 adaptively. This semiparametric approach exactly generalizes the local FDR procedure (Efron et al., 2001) and connects with the BH procedure (Benjamini & Hochberg, 1995). A variety of simulations show that our semiparametric approach outperforms classical procedures which assume independence and the parametric approaches which capture dependence.