Stepup procedures controlling generalized FWER and generalized FDR

Abstract

In many applications of multiple hypothesis testing where more than one false rejection can be tolerated, procedures controlling error rates measuring at least $k$ false rejections, instead of at least one, for some fixed $k\ge 1$ can potentially increase the ability of a procedure to detect false null hypotheses. The $k$-FWER, a generalized version of the usual familywise error rate (FWER), is such an error rate that has recently been introduced in the literature and procedures controlling it have been proposed. A further generalization of a result on the $k$-FWER is provided in this article. In addition, an alternative and less conservative notion of error rate, the $k$-FDR, is introduced in the same spirit as the $k$-FWER by generalizing the usual false discovery rate (FDR). A $k$-FWER procedure is constructed given any set of increasing constants by utilizing the $k$th order joint null distributions of the $p$-values without assuming any specific form of dependence among all the $p$-values. Procedures controlling the $k$-FDR are also developed by using the $k$th order joint null distributions of the $p$-values, first assuming that the sets of null and nonnull $p$-values are mutually independent or they are jointly positively dependent in the sense of being multivariate totally positive of order two (MTP${}_2$) and then discarding that assumption about the overall dependence among the $p$-values.

Published in at http://dx.doi.org/10.1214/009053607000000398 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• Generalizations of the Familywise Error Rate
• A stochastic process approach to false discovery control
• Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses
• False discovery and false nondiscovery rates in single-step multiple testing procedures
• Stepup procedures controlling generalized FWER and generalized FDR

Cited by in corpus (9)

• Stepup procedures controlling generalized FWER and generalized FDR
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• New procedures controlling the false discovery proportion via Romano-Wolf's heuristic
• Selective conformal inference with false coverage-statement rate control
• Graphical approaches for the control of generalised error rates
• Classes of Multiple Decision Functions Strongly Controlling FWER and FDR