Asymptotic properties of a two sample randomized test for partially dependent data

We are concerned with an issue of asymptotic validity of a non-parametric randomization test for the two sample location problem under the assumption of partially dependent observations, in which case the validity of the usual permutation tt-test breaks down. We show that a certain modification of the permutation group used in the randomization procedure yields an unconditional asymptotically valid test in the sense that its probability of Type I error tends to the nominal level with increasing sample sizes. We show that this unconditional test is equivalent to the one based on a linear combination of two- and one-sample tt-statistics and enjoys some optimal power properties. We also conduct a simulation study comparing our approach with that based on the Fisher's method of combining pp-values. Finally, we present an example of application of the test in a medical study on functional status assessment at the end of life.