Copula–Induced Measures of Concordance

Sebastian Fuchs. "Copula–Induced Measures of Concordance." Dependence Modeling 4.1 (2016): 205-214, electronic only. <http://eudml.org/doc/287103>.

@article{SebastianFuchs2016,
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.},
author = {Sebastian Fuchs},
journal = {Dependence Modeling},
keywords = {copulas; transformations of copulas; measures of concordance},
language = {eng},
number = {1},
pages = {205-214, electronic only},
title = {Copula–Induced Measures of Concordance},
url = {http://eudml.org/doc/287103},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Sebastian Fuchs
TI - Copula–Induced Measures of Concordance
JO - Dependence Modeling
PY - 2016
VL - 4
IS - 1
SP - 205
EP - 214, electronic only
AB - 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.
LA - eng
KW - copulas; transformations of copulas; measures of concordance
UR - http://eudml.org/doc/287103
ER -