Nonparametric estimator of false discovery rate based on Bernšteǐn polynomials

Under a local dependence assumption about the p-values, an estimator of the proportion TTQ of true null hypotheses, having a closed-form expression, is derived based on Bernstein 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.