A resampling procedure for nonparametric combination of several dependent tests

Summary This paper deals with nonparametric methods for combining dependent permutation or randomization tests. Particularly, they are nonparametric with respect to the underlying dependence structure. The methods are based on a without replacement resampling procedure (WRRP) conditional on the observed data, also called conditional simulation, which provide suitable estimates, as good as computing time permits, of the permutational distribution of any statistic. A class C of combining functions is characterized in such a way that all its members, under suitable and reasonable conditions, are found to be consistent and unbiased. Moreover, for some of its members, their almost sure asymptotic equivalence with respect to best tests, in particular cases, is shown. An applicational example to a multivariate permutationalt-paired test is also discussed.