Title: On the Development of Local FDR-Based Approach to Testing Two-Way Classified Hypotheses
Abstract: Multiple testing of two-way classified hypotheses controlling false discoveries is a commonly encountered statistical problem in modern scientific research. Nevertheless, research focused on developing local FDR (Lfdr) based methods efficiently accommodating such structural information has not yet taken place beyond one-way classification settings. This article takes the first step toward that wider domain. It extends the two-component mixture model (Efron et al., 2001, JASA) from unclassified to two-way classified hypotheses capturing the underlying structure of the hypotheses. The extension provides the foundational framework for the development of newer and potentially powerful Lfdr based multiple testing procedures in their oracle and data-adaptive forms for two-way classified hypotheses.