Spatial extremes: Max-stable processes at work

Ribatet, Mathieu

Journal de la société française de statistique, Tome 154 (2013) no. 2, pp. 156-177.

De nombreux progrès ont été accomplis ces dernières décennies sur la théorie des valeurs extrêmes fonctionnelle. Dans ce papier nous regroupons les résultats principaux concernant les processus max-stables. Ainsi cette revue de littérature couvre une gamme variée de domaines : lois fini-dimensionnelles, modèles paramétriques, mesures de dépendance, procédure inférentielles, sélection de modèles et simulations (conditionnelles). Une application à la modélisation spatiale des rafales de vents aux Pays-bas est donnée.

Since many developments to the functional extreme value theory have been made during the last decades, this paper reviews recent results on max-stable processes and covers a large range of themes such as finite dimensional distributions, parametric models, dependence measure, inferential procedure, model selection and (conditional) simulations. An application to the spatial modeling of wind gusts in Netherlands is given.

Keywords: Max-stable process, Extremal coefficient function, Composite likelihood, Simulation
Mot clés : Processus max-stable, Fonction du coefficient extrême, Vraisemblance composite, Simulation

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