Imperial College London
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Professor Axel Gandy

Faculty of Natural Sciences, Department of Mathematics

Head of Department of Mathematics & Chair in Statistics
 
 
 
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Contact

 

+44 (0)20 7594 8518a.gandy Website

 
 
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Location

 

644Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Gandy:2011:10.1214/12-AOS1076,
author = {Gandy, A and Rubin-Delanchy, P},
doi = {10.1214/12-AOS1076},
title = {An algorithm to compute the power of Monte Carlo tests with guaranteed  precision},
url = {http://dx.doi.org/10.1214/12-AOS1076},
year = {2011}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - This article presents an algorithm that generates an exact (conservative)confidence interval of a specified length and coverage probability for thepower of a Monte Carlo test (such as a bootstrap or permutation test). It isthe first method that achieves this aim for almost any Monte Carlo test. Theexisting research on power estimation for Monte Carlo tests has focused onobtaining as accurate a result as possible for a fixed computational effort.However, the methods proposed do not provide any guarantee of precision, in thesense that they cannot report a confidence interval to accompany their estimateof the power. Conversely in this article the computational effort is random.The algorithm operates until a confidence interval can be constructed thatmeets the requirements of the user, in terms of length and coverageprobability. We show that, surprisingly, by generating two more datasets thatwhat might have been assumed to be sufficient, the expected number of stepsrequired by the algorithm is finite in many cases of practical interest. Theseinclude, for instance, any situation where the distribution of the p-value isabsolutely continuous or if it is discrete with finite support. The algorithmis implemented in the R package simctest.
AU  - Gandy,A
AU  - Rubin-Delanchy,P
DO  - 10.1214/12-AOS1076
PY  - 2011///
TI  - An algorithm to compute the power of Monte Carlo tests with guaranteed  precision
UR  - http://dx.doi.org/10.1214/12-AOS1076
UR  - http://arxiv.org/abs/1110.1248v1
UR  - http://hdl.handle.net/10044/1/18651
ER  -
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