Asymptotic dependence of bivariate maxima

Abstract

The Ledford and Tawn model for the bivariate tail incorporates a coefficient, η, 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.

Keywords:

• Extreme value theory
• stationary sequences
• asymptotic dependence
• dependence conditions

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 60G70

Acknowledgments

The authors would like to thank the reviewers for their valuable comments that contributed to improve this article. The first author’s research was partially supported by the research unit UID/MAT/00212/2013. The second author was financed by Portuguese Funds through FCT–Fundação para a Ciência e a Tecnologia within the Projects UID/MAT/00013/2013, UID/MAT/00006/2013 and by the research center CEMAT (Instituto Superior Técnico, Universidade de Lisboa) through the Project UID/Multi/04621/2013.