Statistics – Computation
Scientific paper
2011-10-06
Statistics
Computation
27 pages, 7 figures
Scientific paper
This article presents an algorithm that generates an exact (conservative) confidence interval of a specified length and coverage probability for the power of a Monte Carlo test (such as a bootstrap or permutation test). It is the first method that achieves this aim for almost any Monte Carlo test. The existing research on power estimation for Monte Carlo tests has focused on obtaining as accurate a result as possible for a fixed computational effort. However, the methods proposed do not provide any guarantee of precision, in the sense that they cannot report a confidence interval to accompany their estimate of the power. Conversely in this article the computational effort is random. The algorithm operates until a confidence interval can be constructed that meets the requirements of the user, in terms of length and coverage probability. We show that, surprisingly, by generating two more datasets that what might have been assumed to be sufficient, the expected number of steps required by the algorithm is finite in many cases of practical interest. These include, for instance, any situation where the distribution of the p-value is absolutely continuous or if it is discrete with finite support. The algorithm is implemented in the R package simctest.
Gandy Axel
Rubin-Delanchy Patrick
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