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.
@article{bwmeta1.element.doi-10_1515_demo-2016-0011,
author = {Sebastian Fuchs},
title = {Copula--Induced Measures of Concordance},
journal = {Dependence Modeling},
volume = {4},
year = {2016},
zbl = {1349.62237},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_demo-2016-0011}
}
Sebastian Fuchs. Copula–Induced Measures of Concordance. Dependence Modeling, Tome 4 (2016) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_demo-2016-0011/