Abstract: Under a local dependence assumption about the -values, an estimator of the proportion of true null hypotheses, having a closed-form expression, is derived based on Bernštein 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 and the FDR are also given. The usefulness of the proposed method is demonstrated through simulations and its application to a microarray dataset.
Key words and phrases: Bernštein polynomials, bioinformatics, density estimation, false discovery rate, local dependence, microarray, mixture model, multiple comparison.