Optimal number of upper order statistics used in estimation for the coeffcient of tail dependence

Abstract

Beirlant et al. (2011) introduced a bias-reduced estimator for the coeffcient of tail dependence and for bivariate tail probability in bivariate extreme value statistics. In this paper, we are interested in the problem of choice of the number of extreme order statistics of bivariate observations exceeding high thresholds, we want to optimize the estimators on the choice we expose different methods for determining this number. The effciency of our methods is illustrated on a simulation study and by an application to real data.

Keywords: Coeffcient of tail dependence; Bias reduction; Extended Pareto distribution; Tail probability; Copula; Hill estimator; Moment estimator