Moment-based multivariate permutation tests for ordinal categorical data

Stochastic dominance problems in testing for ordered categorical variables are of specific interest in performance analysis, because they are frequently encountered in practice and present distinctive difficulties, especially within the framework of likelihood ratio tests. Until now, the literature has essentially considered the univariate case, and several solutions have been proposed to cope with it, most of which are based on restricted maximum likelihood ratio tests. These solutions are generally criticised, because the degree of accuracy of their asymptotic null and alternative distributions is difficult to assess and characterise. In this paper, we propose a new exact solution based on a simultaneous analysis of a finite set of sampling moments of ranks, or general scores, assigned to ordered classes and processed within a permutation approach.