Multiple Testing under Dependence via Semiparametric Graphical Models.

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.