Sampling spatial structures in geostatistical framework

TL;DR

This paper introduces new models for extremal coefficients, extremograms, and cross-extremograms within a spatial geostatistical framework, utilizing extremal variograms to characterize asymptotic behaviors of spatial phenomena.

Contribution

It develops novel models for extremal dependence measures in spatial fields based on copulas and extremal variograms, advancing spatial extreme value analysis.

Findings

New models for extremal coefficients in spatial fields

Extensions of extremogram and cross-extremogram models

Use of extremal variogram to characterize asymptotic behavior

Abstract

Extreme values geostatistics make it possible to model the asymptotic behaviors of random phenomena which depends on space or time parameters. In this paper, we propose new models of the extremal coefficient within a spatial stationary fields underlied by multivariate copulas. Some models of extensions of the extremogram and the cross-extremogram are constructed in a spatial framework. Moreover, both these two geostatistcal tools are modeled using the extremal variogram which characterizes the asymptotic stochastic behavior of the phenomena.