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June 2014 Further results on controlling the false discovery proportion
Wenge Guo, Li He, Sanat K. Sarkar
Ann. Statist. 42(3): 1070-1101 (June 2014). DOI: 10.1214/14-AOS1214

Abstract

The probability of false discovery proportion (FDP) exceeding $\gamma\in[0,1)$, defined as $\gamma$-FDP, has received much attention as a measure of false discoveries in multiple testing. Although this measure has received acceptance due to its relevance under dependency, not much progress has been made yet advancing its theory under such dependency in a nonasymptotic setting, which motivates our research in this article. We provide a larger class of procedures containing the stepup analog of, and hence more powerful than, the stepdown procedure in Lehmann and Romano [Ann. Statist. 33 (2005) 1138–1154] controlling the $\gamma$-FDP under similar positive dependence condition assumed in that paper. We offer better alternatives of the stepdown and stepup procedures in Romano and Shaikh [IMS Lecture Notes Monogr. Ser. 49 (2006a) 33–50, Ann. Statist. 34 (2006b) 1850–1873] using pairwise joint distributions of the null $p$-values. We generalize the notion of $\gamma$-FDP making it appropriate in situations where one is willing to tolerate a few false rejections or, due to high dependency, some false rejections are inevitable, and provide methods that control this generalized $\gamma$-FDP in two different scenarios: (i) only the marginal $p$-values are available and (ii) the marginal $p$-values as well as the common pairwise joint distributions of the null $p$-values are available, and assuming both positive dependence and arbitrary dependence conditions on the $p$-values in each scenario. Our theoretical findings are being supported through numerical studies.

Citation

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Wenge Guo. Li He. Sanat K. Sarkar. "Further results on controlling the false discovery proportion." Ann. Statist. 42 (3) 1070 - 1101, June 2014. https://doi.org/10.1214/14-AOS1214

Information

Published: June 2014
First available in Project Euclid: 20 May 2014

zbMATH: 1305.62271
MathSciNet: MR3210996
Digital Object Identifier: 10.1214/14-AOS1214

Subjects:
Primary: 62J15

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 3 • June 2014
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