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Journal of Probability and Statistics
Volume 2016, Article ID 3937056, 7 pages
Research Article

Estimating the Proportion of True Null Hypotheses in Multiple Testing Problems

1Manufacturing, Toxicology and Applied Statistical Sciences, Janssen Research & Development, Spring House, PA 19002, USA
2Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA

Received 26 July 2016; Revised 19 October 2016; Accepted 8 November 2016

Academic Editor: Shein-chung Chow

Copyright © 2016 Oluyemi Oyeniran and Hanfeng Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The problem of estimating the proportion, , of the true null hypotheses in a multiple testing problem is important in cases where large scale parallel hypotheses tests are performed independently. While the problem is a quantity of interest in its own right in applications, the estimate of can be used for assessing or controlling an overall false discovery rate. In this article, we develop an innovative nonparametric maximum likelihood approach to estimate . The nonparametric likelihood is proposed to be restricted to multinomial models and an EM algorithm is also developed to approximate the estimate of . Simulation studies show that the proposed method outperforms other existing methods. Using experimental microarray datasets, we demonstrate that the new method provides satisfactory estimate in practice.