| Abstract: | In recent years permutation testing methods have increased both in number of applications and in solving complex multivariate
problems. When available permutation tests are essentially of an exact nonparametric nature in a conditional context, where
conditioning is on the pooled observed data set which is often a set of sufficient statistics in the null hypothesis. Whereas,
the reference null distribution of most parametric tests is only known asymptotically. Thus, for most sample sizes of practical
interest, the possible lack of efficiency of permutation solutions may be compensated by the lack of approximation of parametric
counterparts. There are many complex multivariate problems, quite common in empirical sciences, which are difficult to solve
outside the conditional framework and in particular outside the method of nonparametric combination (NPC) of dependent permutation
tests. In this paper we review such a method and its main properties along with some new results in experimental and observational
situations (robust testing, multi-sided alternatives and testing for survival functions). |
