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Dependence Modeling

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Copula–Induced Measures of Concordance

Sebastian Fuchs
Published Online: 2016-10-07 | DOI: https://doi.org/10.1515/demo-2016-0011

Abstract

We study measures of concordance for multivariate copulas and copulas that induce measures of concordance. To this end, for a copula A, we consider the maps C → R given by

where C denotes the collection of all d–dimensional copulas, M is the Fréchet–Hoeffding upper bound, Π is the product copula, [. , .] : C × C → R is the biconvex form given by [C, D] := ∫ [0,1]d C(u) dQD(u) with the probability measure QD associated with the copula D, and ψΛ C → C is a transformation of copulas. We present conditions on ψΛ and on A under which these maps are measures of concordance. The resulting class of measures of concordance is rich and includes the well–known examples Spearman’s rho and Gini’s gamma.

Keywords: copulas; transformations of copulas; measures of concordance

References

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About the article

Received: 2016-04-13

Accepted: 2016-08-04

Published Online: 2016-10-07


Citation Information: Dependence Modeling, Volume 4, Issue 1, ISSN (Online) 2300-2298, DOI: https://doi.org/10.1515/demo-2016-0011.

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© 2016 Sebastian Fuchs. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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