Spatial Extremes: Models for the Stationary Case
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]....
| Veröffentlicht in: | The Annals of Statistics. - Institute of Mathematical Statistics. - 34(2006), 1, Seite 146-168 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2006
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| Zugriff auf das übergeordnete Werk: | The Annals of Statistics |
| Schlagworte: | Extreme-value theory Spatial extremes Spatial tail dependence Maxstable processes Multivariate extremes Semiparametric estimation Mathematics Information science Applied sciences Physical sciences |
| Zusammenfassung: | 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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| ISSN: | 00905364 |