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.
Cite
@article{arxiv.math/0605436,
title = {Spatial extremes: Models for the stationary case},
author = {Laurens de Haan and Teresa T. Pereira},
journal= {arXiv preprint arXiv:math/0605436},
year = {2007}
}
Comments
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)