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A framework for Monte Carlo based multiple testing

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Title: A framework for Monte Carlo based multiple testing
Authors: Gandy, A
Hahn, G
Item Type: Journal Article
Abstract: We are concerned with multiple testing in the setting where p-values are unknown and can only be approximated using Monte Carlo simulation. This scenario occurs widely in practice. We are interested in obtaining the same rejections and non-rejections as the ones obtained if the p-values for all hypotheses had been available. The present article introduces a framework for this scenario by providing a generic algorithm for a general multiple testing procedure. We establish conditions which guarantee that the rejections and non-rejections obtained through Monte Carlo simulations are identical to the ones obtained with the p-values. Our framework is applicable to a general class of step-up and step-down procedures which includes many established multiple testing corrections such as the ones of Bonferroni, Holm, Sidak, Hochberg or Benjamini-Hochberg. Moreover, we show how to use our framework to improve algorithms available in the literature in such a way as to yield theoretical guarantees on their results. These modifications can easily be implemented in practice and lead to a particular way of reporting multiple testing results as three sets together with an error bound on their correctness, demonstrated exemplarily using a real biological dataset.
Issue Date: 14-Apr-2016
Date of Acceptance: 20-Jan-2016
URI: http://hdl.handle.net/10044/1/29045
DOI: https://dx.doi.org/10.1111/sjos.12228
ISSN: 1467-9469
Publisher: Wiley
Start Page: 1046
End Page: 1063
Journal / Book Title: Scandinavian Journal of Statistics
Volume: 43
Issue: 4
Copyright Statement: © 2016 Board of the Foundation of the Scandinavian Journal of Statistics. This is the peer reviewed version of the following article: A framework for Monte Carlo based multiple testing, which has been accepted for publication in the journal Scandinavian Journal of Statistics, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1111/sjos.12228/abstract
Keywords: stat.ME
Statistics & Probability
0104 Statistics
Publication Status: Published
Appears in Collections:Statistics
Faculty of Natural Sciences