Bivariate tail estimation: dependence in asymptotic independence

Abstract

In the classical setting of bivariate extreme value theory, the procedures for estimating the probability of an extreme event are not applicable if the componentwise maxima of the observations are asymptotically independent. To cope with this problem, Ledford and Tawn proposed a submodel in which the penultimate dependence is characterized by an additional parameter. We discuss the asymptotic properties of two estimators for this parameter in an extended model. Moreover, we develop an estimator for the probability of an extreme event that works in the case of asymptotic independence as well as in the case of asymptotic dependence, and prove its consistency.