Bernoulli

  • Bernoulli
  • Volume 13, Number 1 (2007), 229-251.

Estimating the tail dependence function of an elliptical distribution

Claudia Klüppelberg, Gabriel Kuhn, and Liang Peng

Full-text: Open access

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.

Article information

Source
Bernoulli, Volume 13, Number 1 (2007), 229-251.

Dates
First available in Project Euclid: 30 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1175287731

Digital Object Identifier
doi:10.3150/07-BEJ6047

Mathematical Reviews number (MathSciNet)
MR2307405

Zentralblatt MATH identifier
1111.62048

Keywords
asymptotic normality elliptical distribution regular variation tail dependence function

Citation

Klüppelberg, Claudia; Kuhn, Gabriel; Peng, Liang. Estimating the tail dependence function of an elliptical distribution. Bernoulli 13 (2007), no. 1, 229--251. doi:10.3150/07-BEJ6047. https://projecteuclid.org/euclid.bj/1175287731


Export citation