Title: Adaptive p-value weighting with power optimality,
Abstract: Weighting the p-values is a well-established strategy that improves the power
of multiple testing procedures while dealing with heterogeneous data. However,
how to achieve this task in an optimal way is rarely considered in the
literature. This paper contributes to fill the gap in the case of
group-structured null hypotheses, by introducing a new class of procedures
named ADDOW (for Adaptive Data Driven Optimal Weighting) that adapts both to
the alternative distribution and to the proportion of true null hypotheses. We
prove the asymptotical FDR control and power optimality among all weighted
procedures of ADDOW, which shows that it dominates all existing procedures in
that framework. Some numerical experiments show that the proposed method
preserves its optimal properties in the finite sample setting when the number
of tests is moderately large.