Bias and variance reduction in estimating the proportion of true-null hypotheses

Abstract

When testing a large number of hypotheses, estimating the proportion of true nulls, denoted by π(0), becomes increasingly important. This quantity has many applications in practice. For instance, a reliable estimate of π(0) can eliminate the conservative bias of the Benjamini-Hochberg procedure on controlling the false discovery rate. It is known that most methods in the literature for estimating π(0) are conservative. Recently, some attempts have been paid to reduce such estimation bias. Nevertheless, they are either over bias corrected or suffering from an unacceptably large estimation variance. In this paper, we propose a new method for estimating π(0) that aims to reduce the bias and variance of the estimation simultaneously. To achieve this, we first utilize the probability density functions of false-null p-values and then propose a novel algorithm to estimate the quantity of π(0). The statistical behavior of the proposed estimator is also investigated. Finally, we carry out extensive simulation studies and several real data analysis to evaluate the performance of the proposed estimator. Both simulated and real data demonstrate that the proposed method may improve the existing literature significantly.

Keywords: Effect size; False-null p-value; Microarray data; Multiple testing; Probability density function; Upper tail probability.