Numéro spécial : statistique des valeurs extrêmes
Measuring and modelling multivariate and spatial dependence of extremes
Journal de la société française de statistique, Volume 154 (2013) no. 2, pp. 139-155.

Within both multivariate extreme models and spatial processes, it is important to precisely identify dependencies among extremes. In particular detecting asymptotic independence is fundamental and in a multivariate setting, many authors have proposed measures of extreme dependence/independence with sometimes associated tests. Dependence structures within spatial processes are more complex and very few authors have considered other structures than the max-stable one. In this survey paper some major contributions to inference and modelling for extremal dependencies are presented in multivariate and spatial contexts, including the presentation of recent spatial models allowing asymptotic independence.

Lorsque l’on s’intéresse aux extrêmes multivariés ou spatiaux, il est important d’identifier au mieux la nature des dépendances entre réalisations extrêmes. La notion d’indépendance asymptotique des extrêmes est à ce titre primordiale. Dans un cadre multivarié, différentes mesures quantifiant la dépendance extrêmale ont été proposées et des tests d’indépendance asymptotique mis en oeuvre. Pour le cadre spatial, la modélisation classique s’appuie sur les processus max-stables mais les structures de dépendance présentes peuvent être plus complexes que celles gérées par ce type de processus. Dans cet article, les principaux résultats sur l’inférence et la modélisation de la dépendance entre réalisations extrêmes sont présentés et l’accent est mis sur les modèles récents permettant une prise en compte de l’indépendance asymptotique.

Keywords: Asymptotic dependence/independence, Multivariate extreme dependence, Spatial extreme dependence, Max-stable process, Inverse max-stable process
Mot clés : Dépendance/Indépendance asymptotique, Dépendance extrême multivariée, Dépendance extrême spatiale, Processus max-stable, Processus inverse max-stable
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Bacro, Jean-Noël; Toulemonde, Gwladys. Measuring and modelling multivariate and spatial dependence of extremes. Journal de la société française de statistique, Volume 154 (2013) no. 2, pp. 139-155. http://www.numdam.org/item/JSFS_2013__154_2_140_0/

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