Max-stable processes for modelling extremes observed in space and time

By Richard A. Davis, Claudia Klüppelberg, C. Steinkohl. 2011

55 citations recorded by the source corpus.

Abstract Max-stable processes have proved to be useful for the statistical modeling of spatial extremes. For statistical inference it is often assumed that there is no temporal dependence; i.e., that the observations at spatial locations are independent in time. In a first approach we construct max-stable space–time processes as limits of rescaled pointwise maxima of independent Gaussian processes, where the space–time covariance functions satisfy weak regularity conditions. This leads to so-called Brown–Resnick processes. In a second approach, we extend Smith’s storm profile model to a space–time setting. We provide explicit expressions for the bivariate distribution functions, which are equal under appropriate choice of the parameters. We also show how the space–time covariance function of the underlying Gaussian process can be interpreted in terms of the tail dependence function in the limiting max-stable space–time process.

Subfields: Economics and Econometrics, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cfefb78eee57625525421c4e40268820bfa20d02

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Raphaël Huser
2. A. C. Davison
3. Thomas Opitz
4. Claudia Klüppelberg
5. C. Steinkohl
6. Richard A. Davis
7. H. Bakka
8. Håvard Rue

In Environmental Engineering

1. Raphaël Huser
2. Thomas Opitz
3. A. C. Davison
4. H. Bakka
5. Richard A. Davis
6. Håvard Rue
7. Claudia Klüppelberg
8. C. Steinkohl

In Statistics and Probability

1. Raphaël Huser
2. Thomas Opitz
3. A. C. Davison
4. Claudia Klüppelberg
5. H. Bakka
6. C. Steinkohl
7. Richard A. Davis
8. Håvard Rue

Citations in the corpus

• Statistical inference for max‐stable processes in space and time (2012, methodology): “The following proposition is a space–time extension of a result in Kabluchko et al. (2009), which was also considered in Davis et al. (2011).”
• Space–time modelling of extreme events (2012, background): “The function ρ must therefore be a valid space-time correlation function (Gneiting, 2002; Cressie and Huang, 1999; Davis et al., 2011).”
• INLA goes extreme: Bayesian tail regression for the estimation of high spatio-temporal quantiles (2018, background): “Later, Hosking and Wallis (1987) and Davison and Smith (1990), among others, developed statistical models and methods for extreme events based on either a limiting point process representation or on the related generalized Pareto (GP) distribution.”