On stepdown control of the false discovery proportion

By Joseph P. Romano, A. Shaikh. 2006

56 citations recorded by the source corpus.

Consider the problem of testing multiple null hypotheses. A clas- sical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probabil- ity of even one false rejection. However, if s is large, control of the FWER is so stringent that the ability of a procedure which controls the FWER to detect false null hypotheses is limited. Consequently, it is desirable to consider other measures of error control. We will consider methods based on control of the false discovery proportion (FDP) defined by the number of false rejec- tions divided by the total number of rejections (defined to be 0 if there are no rejections). The false discovery rate proposed by Benjamini and Hochberg (1995) controls E(FDP). Here, we construct methods such that, for any and �, P {FDP > } ≤ �. Based on p-values of individual tests, we consider stepdown procedures that control the FDP, without imposing dependence as- sumptions on the joint distribution of the p-values. A greatly improved version of a method given in Lehmann and Romano (10) is derived and generalized to provide a means by which any sequence of nondecreasing constants can be rescaled to ensure control of the FDP. We also provide a stepdown procedure that controls the FDR under a dependence assumption.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/60492d293bfd7257c5b6099cb0c44b48fb7d04b8

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In Management Science and Operations Research

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Citations in the corpus

Control of the false discovery rate under dependence using the bootstrap and subsampling (2008, methodology): “hypothesis are discussed in Lehmann and Romano (2005a), Romano and Shaikh (2006a) , and”
Control of generalized error rates in multiple testing (2007, methodology): “Some more conservative methods that hold under no dependence assumptions are also developed in [17, 25] and [26].”
Multiple hypothesis testing in experimental economics (2019, methodology): “The multiple testing issue is well known in the econometric theory field (e.g. Romano and Wolf, 2005a,b; Romano and Shaikh, 2006b; Romano et al., 2008b) and the biostatistics literature (e.g. Hochberg, 1988; O’Brien, 1984; Marcus et al., 1976).”
Two simple sufficient conditions for FDR control (2008, methodology): “…can be relevant for instance when the underlying obervation is modelled as a stochastic process); • the results of Benjamini and Liu (1999a) and Romano and Shaikh (2006a) on a speciﬁc type of step-down procedure are extended to the cases of positive dependencies (under a PRDS-type condition)…”
Balanced Control of Generalized Error Rates (2010, background): “(2005a), Romano and Shaikh (2006a) , and Romano and Shaikh (2006b).”