Estimation of Proportion of Null Hypotheses Under Dependence

TL;DR

This paper examines how existing methods for estimating the proportion of null hypotheses perform under dependence, focusing on the asymptotic behavior of the BH estimator and evaluating alternative estimators in dependent scenarios.

Contribution

It provides an analysis of the asymptotic properties of the BH estimator under dependence and compares it with other estimators like Storey's and Patra and Sen's in such settings.

Findings

BH estimator's asymptotic behavior under dependence analyzed

Performance of Storey's and Patra and Sen's estimators evaluated in dependent scenarios

Insights into estimator effectiveness for dependent multiple testing problems

Abstract

Estimation of the proportion of null hypotheses in a multiple testing problem can greatly enhance the performance of the existing algorithms. Although various estimators for the proportion of null hypotheses have been proposed, most are designed for independent samples, and their effectiveness in dependent scenarios is not well explored. This article investigates the asymptotic behavior of the BH estimator and evaluates its performance across different types of dependence. Additionally, we assess Storey's estimator and another estimator proposed by Patra and Sen (2016) to understand their effectiveness in these settings.