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Journal of Probability and Statistics
Volume 2012, Article ID 320425, 19 pages
Research Article

Control of the False Discovery Proportion for Independently Tested Null Hypotheses

1Department of Neurology, Mount Sinai School of Medicine, One Gustave L. Levy Place, P.O. Box 1137, New York, NY 10029, USA
2Division of Biostatistics, School of Medicine, New York University, 650 First Avenue, 5th Floor, New York, NY 10016, USA

Received 14 December 2011; Accepted 8 February 2012

Academic Editor: Yongzhao Shao

Copyright © 2012 Yongchao Ge and Xiaochun Li. 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.


Consider the multiple testing problem of testing m null hypotheses H1,,Hm, among which m0 hypotheses are truly null. Given the P-values for each hypothesis, the question of interest is how to combine the P-values to find out which hypotheses are false nulls and possibly to make a statistical inference on m0. Benjamini and Hochberg proposed a classical procedure that can control the false discovery rate (FDR). The FDR control is a little bit unsatisfactory in that it only concerns the expectation of the false discovery proportion (FDP). The control of the actual random variable FDP has recently drawn much attention. For any level 1α, this paper proposes a procedure to construct an upper prediction bound (UPB) for the FDP for a fixed rejection region. When 1α=50%, our procedure is very close to the classical Benjamini and Hochberg procedure. Simultaneous UPBs for all rejection regions' FDPs and the upper confidence bound for the unknown m0 are presented consequently. This new proposed procedure works for finite samples and hence avoids the slow convergence problem of the asymptotic theory.