Asymptotic dependence of bivariate maxima

Abstract

The Ledford and Tawn model for the bivariate tail incorporates a coefficient, $\eta$, as a measure of pre-asymptotic dependence between the marginals. However, in the limiting bivariate extreme value model, $G$, of suitably normalized component-wise maxima, it is just a shape parameter without reflecting any description of the dependency in $G$. Under some local dependence conditions, we consider an index that describes the pre-asymptotic dependence in this context. We analyze some particular cases considered in the literature and illustrate with examples. A small discussion on inference is presented at the end.