Extremal behaviour of aggregated data with an application to downscaling

• 成果类型: Article
• 署名作者: Engelke, Sebastian; De Fondeville, Raphael; Oesting, Marco
• 署名单位: University of Geneva; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Universitat Siegen
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asy052
• 发表日期: 2019
• 页码: 127144
• 关键词: simulation; inference; INDEPENDENCE; VALUES; peaks

摘要

The distribution of spatially aggregated data from a stochastic process may exhibit tail behaviour different from that of its marginal distributions. For a large class of aggregating functionals we introduce the -extremal coefficient, which quantifies this difference as a function of the extremal spatial dependence in . We also obtain the joint extremal dependence for multiple aggregation functionals applied to the same process. Formulae for the -extremal coefficients and multivariate dependence structures are derived in important special cases. The results provide a theoretical link between the extremal distribution of the aggregated data and the corresponding underlying process, which we exploit to develop a method for statistical downscaling. We apply our framework to downscale daily temperature maxima in the south of France from a gridded dataset and use our model to generate high-resolution maps of the warmest day during the heatwave.