Adaptive p-value weighting with power optimality

TL;DR

This paper introduces ADDOW, an adaptive p-value weighting procedure that optimally balances power and false discovery rate control in multiple testing with group-structured hypotheses, outperforming existing methods.

Contribution

The paper proposes ADDOW, a novel data-driven method that adapts to both the alternative distribution and null hypothesis proportion, achieving asymptotic FDR control and power optimality.

Findings

ADDOW controls FDR asymptotically.

ADDOW outperforms existing procedures in power.

Finite sample experiments confirm the method's effectiveness.

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.