Parametric Versus Nonparametrics: Two Alternative Approaches?(with emphasis on permutation methods).

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 especially when the number of observed variables is larger than sample size. In this seminar we discuss this method along with a number of applications in experimental and observational situations (e.g. multi-aspect testing, multivariate stochastic ordering, robust testing, multi-sided alternatives, testing for survival functions).