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Estimating the Tail Dependence Function of an Elliptical Distribution

Claudia Klüppelberg, Gabriel Kuhn and Liang Peng
Bernoulli
Vol. 13, No. 1 (Feb., 2007), pp. 229-251
Stable URL: http://www.jstor.org/stable/25464873
Page Count: 23
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Estimating the Tail Dependence Function of an Elliptical Distribution
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Abstract

Recently there has been growing interest in applying elliptical distributions to risk management. Under certain conditions, Hult and Lindskog 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.

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