Estimating Tail Dependence of Elliptical Distributions

Recently there has been an increasing interest in applying
elliptical distributions to risk management. Under weak conditions,
Hult and Lindskog (2002) showed that a random vector with an
elliptical distribution is in the domain of attraction of a
multivariate extreme value distribution. In this paper we study two
estimators for the tail dependence function, which are based on
extreme value theory and the structure of an elliptical
distribution, respectively. After deriving second order regular
variation estimates and proving asymptotic normality for both
estimators, we show that the estimator based on the structure of an
elliptical distribution is better than that based on extreme value
theory in terms of both asymptotic variance and optimal asymptotic
mean squared error.Our theoretical results are confirmed by a
simulation study.