FDR control for multiple hypothesis testing on composite nulls

TL;DR

This paper develops a method for controlling the false discovery rate in multiple hypothesis testing involving composite nulls, leveraging prior distribution assumptions to improve power over traditional methods.

Contribution

It introduces a novel FDR control procedure that uses empirical distribution constraints, enhancing power when nulls are associated with multiple distributions.

Findings

FDR can be controlled using p-values based on empirical distribution constraints.

Proposed method offers substantially more power than maximum significance level approaches.

Applicable when null hypotheses involve finite sets of distributions.

Abstract

Multiple hypothesis testing often involves composite nulls, i.e., nulls that are associated with two or more distributions. In many cases, it is reasonable to assume that there is a prior distribution on the distributions despite it is unknown. When the number of distributions under true nulls is finite, we show that under the above assumption, the false discover rate (FDR) can be controlled using $p$-values computed under constraints imposed by the empirical distribution of the observations. Comparing to FDR control using $p$-values defined as maximum significance level over all null distributions, the proposed FDR control can have substantially more power.