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.
@article{1146576259,
author = {de Haan, Laurens and Pereira, Teresa T.},
title = {Spatial extremes: Models for the stationary case},
journal = {Ann. Statist.},
volume = {34},
number = {1},
year = {2006},
pages = { 146-168},
language = {en},
url = {http://dml.mathdoc.fr/item/1146576259}
}
de Haan, Laurens; Pereira, Teresa T. Spatial extremes: Models for the stationary case. Ann. Statist., Tome 34 (2006) no. 1, pp. 146-168. http://gdmltest.u-ga.fr/item/1146576259/