Davison, A. C.
Padoan, S. A.
Ribatet, M.
Statistical Modeling of Spatial Extremes
Statistical Science
Statistical Science
Statistical Science
Statistical Science
27
Annual maximum analysis
Bayesian hierarchical model
Brown-Resnick process
composite likelihood
copula
environmental data analysis
Gaussian process
generalized extreme-value distribution
geostatistics
latent variable
max-stable process
statistics of extremes
Max-Stable Processes
Sample Extremes
Likelihood Inference
Wind Speeds
Multivariate
Geostatistics
Dependence
Values
Copulas
Trend
2012
2012
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.
Institute of Mathematical Statistics
0883-4237
Statistical Science
Journal Articles
10.1214/11-STS376