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Title:Estimating tail dependence of elliptical distributions PDF Logo
Authors:Klüppelberg, Claudia
Kuhn, Gabriel
Peng, Liang
Issue Date:2006
Series/Report no.:Discussion paper // Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 470
Abstract: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 chapter 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.
Subjects:asymptotic normality
elliptical distribution
regular variation
tail copula
tail dependence function
Persistent Identifier of the first edition:urn:nbn:de:bvb:19-epub-1838-9
Document Type:Working Paper
Appears in Collections:Discussion papers, SFB 386, LMU München

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