Combination based permutation tests: theory and applications

In recent years permutation testing methods have increased both in number of applications and in solving complex multivariate problems. Permutation tests are essentially of an exact nonparametric nature in a conditional context where conditioning is on the pooled observed data set which is generally a set of sufficient statistics in the null hypothesis.

There are many complex multivariate problems which are difficult to solve outside the conditional framework and in particular outside the nonparametric combination (NPC) of dependent permutation tests method. We discuss this method along with some application in different experimental or observational situations (e.g. in biostatistics).Some recent properties and features of combination-based tests are also presented.