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February 2010 Balanced control of generalized error rates
Joseph P. Romano, Michael Wolf
Ann. Statist. 38(1): 598-633 (February 2010). DOI: 10.1214/09-AOS734


Consider the problem of testing s hypotheses simultaneously. In this paper, we derive methods which control the generalized family-wise error rate given by the probability of k or more false rejections, abbreviated k-FWER. We derive both single-step and step-down procedures that control the k-FWER in finite samples or asymptotically, depending on the situation. Moreover, the procedures are asymptotically balanced in an appropriate sense. We briefly consider control of the average number of false rejections. Additionally, we consider the false discovery proportion (FDP), defined as the number of false rejections divided by the total number of rejections (and defined to be 0 if there are no rejections). Here, the goal is to construct methods which satisfy, for given γ and α, P{FDP>γ}≤α, at least asymptotically. Special attention is paid to the construction of methods which implicitly take into account the dependence structure of the individual test statistics in order to further increase the ability to detect false null hypotheses. A general resampling and subsampling approach is presented which achieves these objectives, at least asymptotically.


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Joseph P. Romano. Michael Wolf. "Balanced control of generalized error rates." Ann. Statist. 38 (1) 598 - 633, February 2010.


Published: February 2010
First available in Project Euclid: 31 December 2009

zbMATH: 1181.62110
MathSciNet: MR2590052
Digital Object Identifier: 10.1214/09-AOS734

Primary: 62J15
Secondary: 62G10

Keywords: bootstrap , false discovery proportion , generalized family-wise error rate , multiple testing , step-down procedure

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 1 • February 2010
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