Extremal behaviour of aggregated data with an application to downscaling. (28th December 2018)

• Record Type: Journal Article
• Authors: Engelke, Sebastian; De Fondeville, Raphaël; Oesting, Marco
• Is Part Of: Biometrika. Volume 106:Number 1(2019:Mar.)
• Page Start: 127
• Page End: 144
• Publication Date: 2018-12-28
• Subjects: Aggregation -- Geostatistics -- Simulation of extreme events -- Spatial extreme -- Threshold exceedance; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asy052
• Languages: English
• ISSNs: 0006-3444

Abstract

SUMMARY: The distribution of spatially aggregated data from a stochastic process $X$ may exhibit tail behaviour different from that of its marginal distributions. For a large class of aggregating functionals $\ell$ we introduce the $\ell$ -extremal coefficient, which quantifies this difference as a function of the extremal spatial dependence in $X$ . We also obtain the joint extremal dependence for multiple aggregation functionals applied to the same process. Formulae for the $\ell$ -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 $2003$ heatwave.