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June 2015 New procedures controlling the false discovery proportion via Romano–Wolf’s heuristic
Sylvain Delattre, Etienne Roquain
Ann. Statist. 43(3): 1141-1177 (June 2015). DOI: 10.1214/14-AOS1302

Abstract

The false discovery proportion (FDP) is a convenient way to account for false positives when a large number $m$ of tests are performed simultaneously. Romano and Wolf [ Ann. Statist. 35 (2007) 1378–1408] have proposed a general principle that builds FDP controlling procedures from $k$-family-wise error rate controlling procedures while incorporating dependencies in an appropriate manner; see Korn et al. [ J. Statist. Plann. Inference 124 (2004) 379–398]; Romano and Wolf (2007). However, the theoretical validity of the latter is still largely unknown. This paper provides a careful study of this heuristic: first, we extend this approach by using a notion of “bounding device” that allows us to cover a wide range of critical values, including those that adapt to $m_{0}$, the number of true null hypotheses. Second, the theoretical validity of the latter is investigated both nonasymptotically and asymptotically. Third, we introduce suitable modifications of this heuristic that provide new methods, overcoming the existing procedures with a proven FDP control.

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Sylvain Delattre. Etienne Roquain. "New procedures controlling the false discovery proportion via Romano–Wolf’s heuristic." Ann. Statist. 43 (3) 1141 - 1177, June 2015. https://doi.org/10.1214/14-AOS1302

Information

Received: 1 June 2014; Revised: 1 December 2014; Published: June 2015
First available in Project Euclid: 15 May 2015

zbMATH: 1320.62128
MathSciNet: MR3346700
Digital Object Identifier: 10.1214/14-AOS1302

Subjects:
Primary: 62H15
Secondary: 60F17

Keywords: equi-correlation , False discovery rate , Gaussian multivariate distribution , multiple testing , Positive dependence , Simes’s inequality

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 3 • June 2015
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