STEPUP PROCEDURES CONTROLLING GENERALIZED FWER AND GENERALIZED FDR

By Sanat K. Sarkar. 2007

90 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c91a14f5a1f3d588c08e9db47093da3cf1c0a493

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Citations in the corpus

Only closed testing procedures are admissible for controlling false discovery proportions (2019, background): “A generalization, k-FWER (Finos and Farcomeni, 2011; Guo et al., 2010; Hommel and Hoffmann, 1988; Lehmann and Romano, 2005; Romano and Shaikh, 2006; Sarkar, 2007), makes sure that, for all θ ∈ Θ,”
Some Results on the Control of the False Discovery Rate under Dependence (2007, background): “A variety of possible Type I error rates have been proposed (see, e.g. Benjamini & Hochberg, 1995; Dudoit et al ., 2004; Lehmann & Romano, 2005; Sarkar, 2005).”
Private False Discovery Rate Control (2015, background): “…there are “too many” p -values in [0 , p ( j ) ] for all of them to correspond to null hypotheses: We have j such p -values, and should attribute no more than jq of these to the true nulls; so if we reject all these j hypotheses we would expect that at most a q fraction correspond to true nulls.”
Generalizing Simes' test and Hochberg's stepup procedure (2008, methodology): “Results in this paper have been used very recently in [4, 17].”
On the Simes inequality and its generalization (2008, methodology): “Most importantly, it is closely linked to the inequality establishing the false discovery rate (FDR) control of the Benjamini and Hochberg [1] procedure (Benjamini and Yekutieli [2] and Sarkar [23, 24]), which as a FDR procedure has received the most attention so far in the multiple testing literatu”