Asymptotic optimality of the Westfall--Young permutation procedure for multiple testing under dependence

By Nicolai Meinshausen, Marloes H. Maathuis, Peter Buhlmann. 2011

59 citations recorded by the source corpus.

Test statistics are often strongly dependent in large-scale multiple testing applications. Most corrections for multiplicity are unduly conservative for correlated test statistics, resulting in a loss of power to detect true positives. We show that the Westfall--Young permutation method has asymptotically optimal power for a broad class of testing problems with a block-dependence and sparsity structure among the tests, when the number of tests tends to infinity.

Subfields: Hardware and Architecture, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fc14992b36f80229598fd8991a4e69787f324e33

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Citations in the corpus

Permutation-based simultaneous confidence bounds for the false discovery proportion (2018, methodology): “The reason is that permutation methods take into account the a priori unknown dependence structure of the p -values (Westfall and Young, 1993; Meinshausen et al., 2011; Hemerik and Goeman, 2018).”
Multiple hypothesis testing in genomics (2014, methodology): “The permutation-based FWER-controlling procedures of Westfall & Young [50] are often more powerful than the methods of the previous sections and have even been shown to be asymptotically optimal for a broad class of correlation structures [51].”
Distribution-free Multiple Testing (2016, methodology): “[23] consider an oracle that provides F, and well as the joint distribution of the P-values indexed by F, and use that oracle information to obtain an optimized single-step procedure for FWER control.”
Statistical significance in high-dimensional linear models (2012, methodology): “…in Section 3 does not provide large improvements in power over the Bonferroni–Holm procedure; our method is closely related to the Westfall–Young procedure which has been shown to be asymptotically optimal for a broad class of high-dimensional problems (Meinshausen, Maathuis, and B¨uhlmann, 2011).”
High-dimensional simultaneous inference with the bootstrap (2016, methodology): “This in turn leads to efficiency gains: The procedure has been proven for certain settings to be (nearly) optimal for controlling the familywise error rate (Meinshausen et al. 2011).”
High-Dimensional Statistics with a View Toward Applications in Biology (2014, methodology): “…leads to FWER control under any dependence structure among the tests, and due to such generality, the method is often overly conservative; the Westfall-Young method (Westfall and Young, 1989) offers an alternative, at least for some cases, which often has better power (Meinshausen et al., 2011).”