On the Development of a Local FDR-Based Approach to Testing Two-Way Classified Hypotheses

Multiple testing of two-way classified hypotheses controlling false discoveries is a commonly encountered statistical problem in modern scientific research. Nevertheless, not much progress has been made yet towards improving existing multiple testing procedures by adequately adjusting them to such structural settings. This paper makes contributions to the development of local false discovery rate (Lfdr) based methodologies under these settings. More specially, it extends the two-component mixture model (Efron et al. J. Am. Statist. Assoc. 96, 1151–1160, 2001) from un-classified to two-way classified hypotheses, which captures the underlying two-way classification structure of the hypotheses and provides the foundational framework for the development of newer and potentially powerful Lfdr-based multiple testing procedures for the hypotheses.