Nonparametric Estimator of False Discovery Rate Based on Bernšteǐn Polynomials

Abstract

Under a local dependence assumption about the p-values, an estimator of the proportion π0 of true null hypotheses, having a closed-form expression, is derived based on Bernšteǐn polynomial density estimation. A nonparametric estimator of false discovery rate (FDR) is then obtained. These estimators are proved to be consistent, asymptotically unbiased, and normal. Confidence intervals for π0 and the FDR are also given. The usefulness of the proposed method is demonstrated through simulations and its application to a microarray dataset. Keywords: Bernsteın polynomials, bioinformatics, density estimation, false discovery rate, local dependence, microarray, mixture model, multiple comparison