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Copula–Induced Measures of Concordance

Copula–Induced Measures of Concordance AbstractWe study measures of concordance for multivariate copulas and copulas that induce measures ofconcordance. To this end, for a copula A, we consider the maps C → R given bywhere 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) withthe 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 resultingclass of measures of concordance is rich and includes the well–known examples Spearman’s rho and Gini’sgamma. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Dependence Modeling de Gruyter

Copula–Induced Measures of Concordance

Fuchs, Sebastian
Dependence Modeling , Volume 4 (1): 1 – Oct 7, 2016
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Publisher
de Gruyter
Copyright
© 2016 Sebastian Fuchs
ISSN
2300-2298
eISSN
2300-2298
DOI
10.1515/demo-2016-0011
Publisher site
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Abstract

AbstractWe study measures of concordance for multivariate copulas and copulas that induce measures ofconcordance. To this end, for a copula A, we consider the maps C → R given bywhere 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) withthe 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 resultingclass of measures of concordance is rich and includes the well–known examples Spearman’s rho and Gini’sgamma.

Journal

Dependence Modeling – de Gruyter

Published: Oct 7, 2016

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