Stepup procedures for control of generalizations of the familywise error rate

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dc.creatorRomano, Joseph P.
dc.creatorShaikh, Azeem M.
dc.date2006-11-09
dc.date.accessioned2026-07-07T08:08:22Z
dc.date.available2026-07-07T08:08:22Z
dc.descriptionConsider the multiple testing problem of testing null hypotheses $H_1,...,H_s$. A classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate ($\mathit{FWER}$), the probability of even one false rejection. But if $s$ is large, control of the $\mathit{FWER}$ is so stringent that the ability of a procedure that controls the $\mathit{FWER}$ to detect false null hypotheses is limited. It is therefore desirable to consider other measures of error control. This article considers two generalizations of the $\mathit{FWER}$. The first is the $k-\mathit{FWER}$, in which one is willing to tolerate $k$ or more false rejections for some fixed $k\geq 1$. The second is based on the false discovery proportion ($\mathit{FDP}$), defined to be the number of false rejections divided by the total number of rejections (and defined to be 0 if there are no rejections). Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289--300] proposed control of the false discovery rate ($\mathit{FDR}$), by which they meant that, for fixed $α$, $E(\mathit{FDP})\leqα$. Here, we consider control of the $\mathit{FDP}$ in the sense that, for fixed $γ$ and $α$, $P\{\mathit{FDP}>γ\}\leq α$. Beginning with any nondecreasing sequence of constants and $p$-values for the individual tests, we derive stepup procedures that control each of these two measures of error control without imposing any assumptions on the dependence structure of the $p$-values. We use our results to point out a few interesting connections with some closely related stepdown procedures. We then compare and contrast two $\mathit{FDP}$-controlling procedures obtained using our results with the stepup procedure for control of the $\mathit{FDR}$ of Benjamini and Yekutieli [Ann. Statist. 29 (2001) 1165--1188].
dc.descriptionPublished at http://dx.doi.org/10.1214/009053606000000461 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0611266
dc.identifierhttp://arxiv.org/abs/math/0611266
dc.identifierAnnals of Statistics 2006, Vol. 34, No. 4, 1850-1873
dc.identifierdoi:10.1214/009053606000000461
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131242
dc.subjectStatistics Theory
dc.subject62J15 (Primary)
dc.titleStepup procedures for control of generalizations of the familywise error rate
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