Generalized madogram and pairwise dependence of maxima over two regions of a random field

TL;DR

This paper introduces a new dependence measure for extreme values over two regions in spatial processes, extending the rac12;-madogram, with estimators and an application to Portuguese precipitation data.

Contribution

It proposes a generalized madogram for pairwise dependence of maxima over regions, extending existing measures and providing estimators with proven asymptotic properties.

Findings

The new measure extends the rac12;-madogram concept.

Estimators are consistent and asymptotically normal.

Application demonstrates usefulness in environmental data analysis.

Abstract

Spatial environmental processes often exhibit dependence in their large values. In order to model such processes their dependence properties must be characterized and quantified. In this paper we introduce a measure that evaluates the dependence among extreme observations located in two separated regions of locations of R^2. We compute the range of this new dependence measure, which extends the existing {\lambda}-madogram concept, and compare it with extremal coefficients, finding generalizations of the known relations in pairwise approach. Estimators for this measure are introduced and asymptotic normality and strong consistency are shown. An application to the annual maxima precipitation in Portuguese regions is presented.