Multivariate measures of concordance

Relationship between multivariate concordance and risk measures

The question about the definition of concordance between random vectors is an open problem because there is not an unanimous opinion about its meaning and its appropriate definition. Also the definition of multivariate risk measures encounters many difficulties. In this paper we want to investigate the relationship between these multivariate measures, essentially based on the relation between r...

Some properties of multivariate measures of concordance

We explore the consequences of a set of axioms which extend Scarsini’s axioms for bivariate measures of concordance to the multivariate case and exhibit the following results: (1) A method of extending measures of concordance from the bivariate case to arbitrarily high dimensions. (2) A formula expressing the measure of concordance of the random vectors (±X1, · · · ,±Xn) in terms of the measure...

Multivariate copulas: Transformations, symmetry, order and measures of concordance

Copula-based Orderings of Multivariate Dependence

In this paper I investigate the problem of de…ning a multivariate dependence ordering. First, I provide a characterization of the concordance dependence ordering between multivariate random vectors with …xed margins. Central to the characterization is a multivariate generalization of a well-known bivariate elementary dependence increasing rearrangement. Second, to order multivariate random vect...

Generalized additive models for conditional dependence structures

We develop a generalized additive modeling framework for taking into account the effect of predictors on the dependence structure between two variables. We consider dependence or concordance measures that are solely functions of the copula, because they contain no marginal information: rank correlation coefficients or tail-dependence coefficients represent natural choices. We propose a maximum ...