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Estimating the tail dependence function of an elliptical distribution. (English) Zbl 1111.62048

Summary: Recently there has been growing interest in applying elliptical distributions to risk management. Under certain conditions, H. Hult and F. Lindskog [Adv. Appl. Probab. 34, No. 3, 587–608 (2002; Zbl 1023.60021)] show 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. 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 simulation study further confirms this.

MSC:

62H12 Estimation in multivariate analysis
62G32 Statistics of extreme values; tail inference
62G20 Asymptotic properties of nonparametric inference

Citations:

Zbl 1023.60021
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