A robust false discovery rate controlling procedure using the empirical likelihood with a fast algorithm

This paper introduces a robust procedure for controlling the false discovery rate utilizing empirical likelihood. Traditional approaches assume a normal or parametric distribution as the null distribution. However, it may be challenging to constrain the null distribution within specific parametric models. We focus on the cases where the null distribution may not precisely follow a normal distribution. Multiple testing procedures based on exact normality can lead to misleading outcomes. To address this issue, we adopt the empirical likelihood to estimate the null distribution. Additionally, we introduce the concept of a pilot distribution to establish constraints on the null distribution, which aids in estimating the empirical null distribution. We present a fast algorithm and provide theoretical justification for its efficiency. Furthermore, simulation studies demonstrate that our method outperforms existing approaches in controlling the false discovery rate. We also include examples involving gene expression data and compare the performance of different methods.