A Change-Point Approach to Estimating the Proportion of False Null Hypotheses in Multiple Testing

TL;DR

This paper introduces a novel change-point based method for estimating the proportion of false null hypotheses in multiple testing, demonstrating superior accuracy and extending to superuniform p-values with theoretical backing.

Contribution

The paper proposes a new change-point approach for estimating false null proportions, including asymptotic theory and applications to high-dimensional data.

Findings

Achieves among the smallest RMSE in simulations

Extends estimation to superuniform p-values

Provides asymptotic theory based on quantile processes

Abstract

For estimating the proportion of false null hypotheses in multiple testing, a family of estimators by Storey (2002) is widely used in the applied and statistical literature, with many methods suggested for selecting the parameter $\lambda$. Inspired by change-point concepts, our new approach to the latter problem first approximates the $p$-value plot with a piecewise linear function with a single change-point and then selects the $p$-value at the change-point location as $\lambda$. Simulations show that our method has among the smallest RMSE across various settings, and we extend it to address the estimation in cases of superuniform $p$-values. We provide asymptotic theory for our estimator, relying on the theory of quantile processes. Additionally, we propose an application in the change-point literature and illustrate it using high-dimensional CNV data.