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Anisotropic Brown-Resnick space-time processes: estimation and model assessment. (English) Zbl 1357.62279

Summary: Spatially isotropic max-stable processes have been used to model extreme spatial or space-time observations. One prominent model is the Brown-Resnick process [B. M. Brown and S. I. Resnick, J. Appl. Probab. 14, 732–739 (1977; Zbl 0384.60055)], which has been successfully fitted to time series, spatial data and space-time data. This paper extends the process to possibly anisotropic spatial structures. For regular grid observations we prove strong consistency and asymptotic normality of pairwise maximum likelihood estimates for fixed and increasing spatial domain, when the number of observations in time tends to infinity. We also present a statistical test for isotropy versus anisotropy. We apply our test to precipitation data in Florida, and present some diagnostic tools for model assessment. Finally, we present a method to predict conditional probability fields and apply it to the data.

MSC:

62M40 Random fields; image analysis
62G32 Statistics of extreme values; tail inference
62P12 Applications of statistics to environmental and related topics
62F05 Asymptotic properties of parametric tests
62F12 Asymptotic properties of parametric estimators
60G70 Extreme value theory; extremal stochastic processes

Citations:

Zbl 0384.60055
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References:

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