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Statistical modeling of spatial extremes. (English) Zbl 1330.86021

Summary: The areal modeling of the extremes of a natural process such as rainfall or temperature is important in environmental statistics; for example, understanding extreme areal rainfall is crucial in flood protection. This article reviews recent progress in the statistical modeling of spatial extremes, starting with sketches of the necessary elements of extreme value statistics and geostatistics. The main types of statistical models thus far proposed, based on latent variables, on copulas and on spatial max-stable processes, are described and then are compared by application to a data set on rainfall in Switzerland. Whereas latent variable modeling allows a better fit to marginal distributions, it fits the joint distributions of extremes poorly, so appropriately-chosen copula or max-stable models seem essential for successful spatial modeling of extremes.

MSC:

86A32 Geostatistics
62M30 Inference from spatial processes
60G70 Extreme value theory; extremal stochastic processes
62G32 Statistics of extreme values; tail inference
62H05 Characterization and structure theory for multivariate probability distributions; copulas

Software:

ismev; spBayes
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Full Text: DOI arXiv Euclid

References:

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