Les attracteurs maximaux des copules bivariées diagonales et de Bertino sont déterminés sous des conditions de régularité idoines. On en déduit des bornes sur l’attracteur maximal d’une copule symétrique à coupe diagonale donnée, ainsi que des bornes sur le rho de Spearman et le tau de Kendall d’une copule de valeurs extrêmes échangeable dont le coefficient de dépendance caudale supérieure est connu. Certains de ces résultats sont ensuite étendus aux cas de copules bivariées quelconques et de copules multivariées.
The maximal attractors of bivariate diagonal and Bertino copulas are determined under suitable regularity conditions. Some consequences of these facts are drawn, namely bounds on the maximal attractor of a symmetric copula with a given diagonal section, and bounds on Spearman’s rho and Kendall’s tau for an exchangeable extreme-value copula whose upper-tail dependence coefficient is known. Some of these results are then extended to the case of arbitrary bivariate copulas and to multivariate copulas.
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@article{CRMATH_2020__358_11-12_1157_0,
author = {Genest, Christian and Sabbagh, Magid},
title = {Comportement extr\'emal des copules diagonales et de {Bertino}},
journal = {Comptes Rendus. Math\'ematique},
pages = {1157--1167},
publisher = {Acad\'emie des sciences, Paris},
volume = {358},
number = {11-12},
year = {2020},
doi = {10.5802/crmath.135},
language = {fr},
url = {http://www.numdam.org/articles/10.5802/crmath.135/}
}
TY - JOUR AU - Genest, Christian AU - Sabbagh, Magid TI - Comportement extrémal des copules diagonales et de Bertino JO - Comptes Rendus. Mathématique PY - 2020 SP - 1157 EP - 1167 VL - 358 IS - 11-12 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.135/ DO - 10.5802/crmath.135 LA - fr ID - CRMATH_2020__358_11-12_1157_0 ER -
%0 Journal Article %A Genest, Christian %A Sabbagh, Magid %T Comportement extrémal des copules diagonales et de Bertino %J Comptes Rendus. Mathématique %D 2020 %P 1157-1167 %V 358 %N 11-12 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.135/ %R 10.5802/crmath.135 %G fr %F CRMATH_2020__358_11-12_1157_0
Genest, Christian; Sabbagh, Magid. Comportement extrémal des copules diagonales et de Bertino. Comptes Rendus. Mathématique, Tome 358 (2020) no. 11-12, pp. 1157-1167. doi : 10.5802/crmath.135. http://www.numdam.org/articles/10.5802/crmath.135/
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