Model-free Bias Reduction of Storey’s Estimator for the Proportion of True Null Hypotheses

Abstract

Storey’s bootstrap estimator for the proportion of true null hypotheses ( π0) has a known bias structure but the amount of bias is obviously unknown. A new method has been proposed in this work to reduce bias of the estimator. The proposed method partitions differential gene expression and similar data sets randomly and repeatedly to first approximate the bias and then corrects it in the final estimate. Unlike some recent developments, the method does not require any model assumption. The proposed method depends on some tuning parameters. For practical applicability of the method, ideal choices of the tuning parameters are given based on numerical results. Extensive simulation experiments show favourable results for the proposed method over the popular robust estimators in the literature. Two real-life microarray data sets have been studied to demonstrate the applicability of the final bias and variance reduced estimator. AMS 2010 subject classifications: 62F10, 62F40