Generating and comparing multivariate ordinal variables by means of permutation tests

We proposed a nonparametric methodology based on partial permutation tests and NPC methodology, to test if data come from an m-dimensional random variable with correlation matrix, R0 D Im where Im is the identity matrix. In particular, we carried out a simulation study in order to compare the performance of the proposed procedures. In this regard we considered simulations from multivariate ordinal variables, generated through a new method recently introduced by [1]. We note that, neither passing from 5 to 7 categories nor passing from a uniform to a symmetric or an asymmetric non-uniform distribution, impacts significantly on the behaviour of the procedures. On the contrary, the structure of the correlation matrix may impact on the performance of the tests, but in most cases the permutation test seems to have the best performance, in particular when the significance level alpha is equal to 0.05 and the sample size is small.