Annals of Statistics

Spatial extremes: Models for the stationary case

Laurens de Haan and Teresa T. Pereira

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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.

Article information

Source
Ann. Statist., Volume 34, Number 1 (2006), 146-168.

Dates
First available in Project Euclid: 2 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1146576259

Digital Object Identifier
doi:10.1214/009053605000000886

Mathematical Reviews number (MathSciNet)
MR2275238

Zentralblatt MATH identifier
1104.60021

Subjects
Primary: 60G70: Extreme value theory; extremal processes 62H11: Directional data; spatial statistics 62G32: Statistics of extreme values; tail inference
Secondary: 62E20: Asymptotic distribution theory 60G10: Stationary processes 62M40: Random fields; image analysis

Keywords
Extreme-value theory spatial extremes spatial tail dependence max-stable processes multivariate extremes semiparametric estimation

Citation

de Haan, Laurens; Pereira, Teresa T. Spatial extremes: Models for the stationary case. Ann. Statist. 34 (2006), no. 1, 146--168. doi:10.1214/009053605000000886. https://projecteuclid.org/euclid.aos/1146576259


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References

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