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On extreme value analysis of a spatial process. (English) Zbl 1153.62074
Summary: One common way to deal with extreme value analysis in spatial statistics is by using the max-stable process. By employing a representation of simple max-stable processes of L. de Haan and A. Ferreira [Extreme value theory. An introduction. NY: Springer (2006; Zbl 1101.62002)], we propose a stationary max-stable process as a model of the dependence structure in two-dimensional spatial problems. We calculate its two-dimensional marginal distributions, which creates the opportunity to estimate the dependence parameter. The model is used by T. A. Buishand, L. de Haan and C. Zhou [On spatial extremes: with application to a rainfall problem. Ann. Appl. Stat., to appear.] for a spatial rainfall problem.

MSC:
62M30 Inference from spatial processes
60G70 Extreme value theory; extremal stochastic processes
62G32 Statistics of extreme values; tail inference
62H10 Multivariate distribution of statistics
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