On the false discovery rate and an asymptotically optimal rejection curve

TL;DR

This paper introduces a new rejection curve for controlling the false discovery rate in multiple testing, providing theoretical guarantees, optimality results, and applications to dependent hypotheses.

Contribution

It proposes a novel rejection curve for FDR control, offers a unifying proof framework allowing dependency, and establishes asymptotic optimality of procedures based on this curve.

Findings

New rejection curve effectively controls FDR asymptotically.

Procedures based on the curve are asymptotically optimal.

Framework accommodates certain dependency structures among hypotheses.

Abstract

In this paper we introduce and investigate a new rejection curve for asymptotic control of the false discovery rate (FDR) in multiple hypotheses testing problems. We first give a heuristic motivation for this new curve and propose some procedures related to it. Then we introduce a set of possible assumptions and give a unifying short proof of FDR control for procedures based on Simes' critical values, whereby certain types of dependency are allowed. This methodology of proof is then applied to other fixed rejection curves including the proposed new curve. Among others, we investigate the problem of finding least favorable parameter configurations such that the FDR becomes largest. We then derive a series of results concerning asymptotic FDR control for procedures based on the new curve and discuss several example procedures in more detail. A main result will be an asymptotic optimality statement for various procedures based on the new curve in the class of fixed rejection curves. Finally, we briefly discuss strict FDR control for a finite number of hypotheses.