The Annals of Statistics

Stepup procedures controlling generalized FWER and generalized FDR

Sanat K. Sarkar

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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≥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 kth 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 kth 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 (MTP2) and then discarding that assumption about the overall dependence among the p-values.

Article information

Ann. Statist., Volume 35, Number 6 (2007), 2405-2420.

First available in Project Euclid: 22 January 2008

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J15: Paired and multiple comparisons 62H15: Hypothesis testing
Secondary: 62H99: None of the above, but in this section

Generalized Holm procedure generalized Hochberg procedure generalized BH procedure generalized BY procedure equicorrelated multivariate normal


Sarkar, Sanat K. Stepup procedures controlling generalized FWER and generalized FDR. Ann. Statist. 35 (2007), no. 6, 2405--2420. doi:10.1214/009053607000000398.

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