On the specification of multivariate association measures and their behaviour with increasing dimension

In this paper the interest is to elaborate on generalization of bivariate association measures, namely Spearman’s rho, Kendall’s tau, Blomqvist’s beta and Gini’s gamma, for a general dimension d≥2. Desirable properties axioms such generalizations are discussed, where special attention given impact addition of: (i) an independent random variable vector; (ii) conical combination all components; (iii) set arbitrary components. Existing evaluated with respect axiom set. For d-variate simplified formula developed, making its analytical computation easier. Further, Archimedean meta-elliptical copulas asymptotic behaviour when d increases studied. Nonparametric estimation considered multivariate measures reviewed nonparametric estimator gamma introduced. The practical use illustrated real data example.