Spatial extremes: Models for the stationary case

Abstract

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.

Published at http://dx.doi.org/10.1214/009053605000000886 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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