A new family of copula-based concordance orderings of random pairs: Properties and nonparametric tests

Abstract

The formal assessment of the stochastic dominance of a random pair with respect to another one is a question of interest in the economic analysis of populations. For example, a manager may wonder if the components of a portfolio are more associated than that of another competing portfolio, in which case the former is generally considered more at risk. In this paper, a new family of copula-based concordance orderings in the spirit of increasing convex and concave orderings of random pairs is introduced as a natural extension of the well-known concordance ordering. In addition, a complete statistical methodology to test the stochastic dominance of a random pair with respect to another one according to the new concordance orderings is developed. The proposed tests are nonparametric, consistent against all alternatives, and valid under serially dependent data satisfying the α-mixing assumption. The sampling properties of the tests are investigated with the help of Monte–Carlo simulations and their usefulness is illustrated on real multivariate data.