Copula–Induced Measures of Concordance

Fuchs Sebastian
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Fuchs Sebastian: Lehrstuhl für Versicherungsmathematik, Technische Universität Dresden

Dependence Modeling, 2016, vol. 4, issue 1, 10

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 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) 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 (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:4:y:2016:i:1:p:10:n:11

DOI: 10.1515/demo-2016-0011

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