Madogram and Asymptotic Independence among Maxima

Abstract

A strong statistical research effort has been devoted in multivariate extreme value theory in order to assess the strength of dependence among extremes. This topic is particularly difficult in the case where block maxima are near independence. In this paper, we adapt and study a simple inference tool inspired from geostatistics, the madogram, to the context of asymptotic independence between pairwise block maxima. In particular, we introduce an extremal coefficient and study the theoretical properties of its estimator. Its behaviour is also illustrated on a small simulation study and a real data set.