Permutation tests for multivariate order-constrained testing problems

This article discusses an effective permutation-based approach to solve order-constrained testing problems, which are very difficult or even impossible to solve within the framework of parametric likelihood. The nonparametric combination (NPC) methodology is a flexible tool which relies on dependent permutation tests and allows us to deal with a large variety of complex testing problems, including the stochastic dominance and monotonic stochastic ordering problems of interest. To deal with them in line with Roy's Union-Intersection (UI) approach, the NPC procedure decomposes the original hypothesis into suitable sub-hypotheses. In this article we discuss and compare two possible types of decomposition, exploiting an extensive simulation study. A real data application is also proposed, in which multivariate ordinal data from the medical field are analyzed.