The Annals of Statistics

Stepup procedures controlling generalized FWER and generalized FDR

Sanat K. Sarkar

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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≥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

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

Dates
First available in Project Euclid: 22 January 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1201012966

Digital Object Identifier
doi:10.1214/009053607000000398

Mathematical Reviews number (MathSciNet)
MR2382652

Zentralblatt MATH identifier
1129.62066

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

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

Citation

Sarkar, Sanat K. Stepup procedures controlling generalized FWER and generalized FDR. Ann. Statist. 35 (2007), no. 6, 2405--2420. doi:10.1214/009053607000000398. https://projecteuclid.org/euclid.aos/1201012966


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