Modified estimator for the proportion of true null hypotheses under discrete setup with proven FDR control by the adaptive Benjamini-Hochberg procedure

TL;DR

This paper introduces a modified estimator for the proportion of true null hypotheses in discrete testing scenarios, demonstrating that the adaptive Benjamini-Hochberg procedure maintains FDR control with this new estimator.

Contribution

It proposes a new estimator for $$ in discrete setups and proves the FDR control of the adaptive BH procedure using this estimator.

Findings

The new estimator is a modification of a popular estimator originally for continuous tests.

The adaptive BH procedure remains conservative with the new estimator.

The paper provides theoretical validation for the estimator's use in discrete testing.

Abstract

Some crucial issues about a recently proposed estimator for the proportion of true null hypotheses ($\pi_0$) under discrete setup are discussed. An estimator for $\pi_0$ is introduced under the same setup. The estimator may be seen as a modification of a very popular estimator for $\pi_0$, originally proposed under the assumption of continuous test statistics. It is shown that adaptive Benjamini-Hochberg procedure remains conservative with the new estimator for $\pi_0$ being plugged in.