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February 2006 Spatial extremes: Models for the stationary case
Laurens de Haan, Teresa T. Pereira
Ann. Statist. 34(1): 146-168 (February 2006). DOI: 10.1214/009053605000000886


The aim of this paper is to provide models for spatial extremes in the case of stationarity. The spatial dependence at extreme levels of a stationary process is modeled using an extension of the theory of max-stable processes of de Haan and Pickands [Probab. Theory Related Fields 72 (1986) 477–492]. We propose three one-dimensional and three two-dimensional models. These models depend on just one parameter or a few parameters that measure the strength of tail dependence as a function of the distance between locations. We also propose two estimators for this parameter and prove consistency under domain of attraction conditions and asymptotic normality under appropriate extra conditions.


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Laurens de Haan. Teresa T. Pereira. "Spatial extremes: Models for the stationary case." Ann. Statist. 34 (1) 146 - 168, February 2006.


Published: February 2006
First available in Project Euclid: 2 May 2006

zbMATH: 1104.60021
MathSciNet: MR2275238
Digital Object Identifier: 10.1214/009053605000000886

Primary: 60G70 , 62G32 , 62H11
Secondary: 60G10 , 62E20 , 62M40

Keywords: extreme-value theory , max-stable processes , multivariate extremes , Semiparametric estimation , spatial extremes , spatial tail dependence

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 1 • February 2006
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