Spatial extremes: Models for the stationary case

Details Spatial extremes: Models for the stationary case Spatial extremes: Models for the stationary case

2006-05-16

arxiv.org/abs/math/0605436v1

Annals of Statistics 2006, Vol. 34, No. 1, 146-168

Mathematics

Statistics Theory

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

Scientific paper

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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