Anisotropic Brown-Resnick space-time processes: estimation and model assessment

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• 作者：Sven Buhl ; Claudia Klüppelberg
• 关键词：Anisotropic space ; time process ; Brown ; Resnick space ; time process ; Hypothesis test for spatial isotropy ; Max ; stable process ; Max ; stable model check ; Pairwise likelihood ; Pairwise maximum likelihood estimate
• 刊名：Extremes
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：19
• 期：4
• 页码：627-660
• 全文大小：1,672 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Quality Control, Reliability, Safety and Risk
  Civil Engineering
  Hydrogeology
  Environmental Management
  Statistics for Business, Economics, Mathematical Finance and Insurance
  
• 出版者：Springer U.S.
• ISSN：1572-915X
• 卷排序：19

文摘

Spatially isotropic max-stable processes have been used to model extreme spatial or space-time observations. One prominent model is the Brown-Resnick process, 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.