An adaptive step-down procedure with proven FDR control under independence

TL;DR

This paper introduces an adaptive step-down procedure for hypothesis testing that guarantees FDR control under independence, demonstrating its effectiveness through theoretical proof and numerical comparisons.

Contribution

It proposes a new adaptive step-down method with proven FDR control under independence, extending the applicability of FDR procedures beyond existing methods.

Findings

The procedure controls FDR at level q for independent test statistics.

It shows competitive power compared to other FDR controlling procedures.

Numerical results confirm FDR control under positive dependence.

Abstract

In this work we study an adaptive step-down procedure for testing $m$ hypotheses. It stems from the repeated use of the false discovery rate controlling the linear step-up procedure (sometimes called BH), and makes use of the critical constants $iq/[(m+1-i(1-q)]$, $i=1,...,m$. Motivated by its success as a model selection procedure, as well as by its asymptotic optimality, we are interested in its false discovery rate (FDR) controlling properties for a finite number of hypotheses. We prove this step-down procedure controls the FDR at level $q$ for independent test statistics. We then numerically compare it with two other procedures with proven FDR control under independence, both in terms of power under independence and FDR control under positive dependence.