On the theory of modified randomization tests for nonparametric hypotheses

A general randomization test for nonparametric hypotheses which is a modification of permutation tests in proposed. The exact level of the test is derived and under mild gegularity conditions, a general result on the consistency of the power function is obtained. Applications to several testing problems are considered. Asymptotic expansions of the power of this test are derived with respect to contiguous alternatives thus test are derived with respect to contiguous alternatives thus enabling us to make deficiency comparisons with permutation tests. The paper concludes with some Monte Carlo simulations verifying the theoretical results derived.