Pointwise estimate of the power and sample size determination for permutation tets

Abstract

A method is presented for the estimation of the power of permutation tests when F is unknown. It is based on the natural plug-in of the empirical distribution in the structure of the statistical test, giving the bootstrap power. The consistency of the permutational bootstrap test is shown. Moreover, to determine the sample size m of permutation tests starting from a pilot sample of size n, the "Mapped Bootstrap" is introduced. The Mapped Bootstrap works for a fixed m and is consistent as the pilot sample size n tends to infinity.