Some properties of multivariate measures of concordance

Details Some properties of multivariate measures of concordance Some properties of multivariate measures of concordance

2008-08-22

arxiv.org/abs/0808.3105v1

Mathematics

Probability

Scientific paper

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 $(\pm X_1,...,\pm X_n)$ in terms of the measures of concordance of the "marginal" random vectors $(X_{i_1},...,X_{i_k})$. (3) A method of expressing the measure of concordance of an odd-dimensional copula in terms of the measures of concordance of its even-dimensional marginals. (4) A family of relations which exist between the measures of concordance of the marginals of a given copula.

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