A Nonparametric Test for the Multivariate Data using the Permutation Principle

In this research, we propose nonparametric tests for the mulativariate data under the two-sample problem setting using the permutation principle for obtaining the null distribution. First we review some well-known testing procedures, which are parametric and nonparametric ones and then compare them with the permutational counterparts. We explain the procedure for applying the permutation principle in some detailed manner. Then we consider to apply the permutation tests to the multivariate data whose components comprised with the continuous and discrete forms to show the volatility of our proposed test procedure. For this purpose, we consider the marginal approach which means that after testing componentwisely, we may combine them together with some suitable combining function. This approach can be applied to the so-called the multivariate one-sided testing problems. Finally we discuss more interesting aspects for the permutation tests as concluding remarks.