Zhong Guan, Baolin Wu and Hongyu Zhao (2008). Nonparametric estimator of false discovery rate based on Bern\v{s}Te\u{i}n polynomials. Vol. 18, No. 3, 905-923.

Statistica Sinica 18(2008), 905-923

NONPARAMETRIC ESTIMATOR OF FALSE DISCOVERY

RATE BASED ON BERNŠTEIN POLYNOMIALS

Zhong Guan, Baolin Wu and Hongyu Zhao

Indiana University South Bend, University of Minnesota

and Yale University School of Medicine

Abstract: Under a local dependence assumption about the -values, an estimator of the proportion $\pi_0$ 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 $\pi_0$ 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.