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This article presents an algorithm that generates a conservative confidenceinterval of a specified length and coverage probability for the power of aMonte Carlo test (such as a bootstrap or permutation test). It is the firstmethod that achieves this aim for almost any Monte Carlo test. Previousresearch has focused on obtaining as accurate a result as possible for a fixedcomputational effort, without providing a guaranteed precision in the abovesense. The algorithm we propose does not have a fixed effort and runs until aconfidence interval with a user-specified length and coverage probability canbe constructed. We show that the expected effort required by the algorithm isfinite in most cases of practical interest, including situations where thedistribution of the p-value is absolutely continuous or discrete with finitesupport. The algorithm is implemented in the R-package simctest, available onCRAN.

An algorithm to compute the power of Monte Carlo tests with guaranteed precision