Dependence of maxima in space

TL;DR

This paper introduces a new dependence coefficient for spatial maxima that measures the strength of dependence among large values, is marginal distribution independent, and relates to existing measures like tail dependence and variograms.

Contribution

It proposes a novel dependence measure for spatial maxima that unifies several properties and can be easily estimated, advancing the analysis of extreme spatial events.

Findings

The coefficient ranges from 0 to 1, with higher values indicating stronger dependence.

It is independent of marginal distributions, making it broadly applicable.

It connects with tail dependence, extremal coefficients, and geostatistical variograms.

Abstract

We propose a coefficient that measures the dependence among large values for spatial processes of maxima. Its main properties are: a) $k$ locations can be taken into account; b) it takes values in $[0,1]$ and higher values indicate stronger dependence; c) it is independent of the univariate marginal distributions of the random field; d) it can be related with the tail dependence and the extremal coefficients; e) it agrees with the concordance property for multivariate distributions; f) it has as a particular case the variogram from geostatistics; g) it can be easily estimated.