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

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 disjoint sets of locations of $\mathbb{R}^2$. 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 the 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.