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A framework for Monte Carlo based multiple testing
File | Description | Size | Format | |
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framework(1).pdf | Accepted version | 285.85 kB | Adobe PDF | View/Open |
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 Mathematics |