Permutation Solutions for Multivariate Ranking and Testing with Applications

In this article, we consider permutation methods for multivariate testing on ordered categorical variables based on the nonparametric combination of permutation dependent tests (NPC; Pesarin and Salmaso, 2010). Furthermore, an extension of the nonparametric combination of dependent rankings (Arboretti et al., 2007) is proposed in order to construct a synthesis of composite indicators. The methodological approaches are applied to a study of risk factors for skin cancer in a cohort of adult patients with heart transplants followed for a minimum of three years after transplantation (Belloni et al, 2004) and to a survey on tourist's opinions about “Tre Cime” Park (District of Sesto Dolomites/Alta Pusteria, Italy).