Estimating the tail dependence function of an elliptical distribution

Claudia Klüppelberg, Gabriel Kuhn, Liang Peng

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

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.

Original languageEnglish
Pages (from-to)229-251
Number of pages23
JournalBernoulli
Volume13
Issue number1
DOIs
StatePublished - 2007

Keywords

  • Asymptotic normality
  • Elliptical distribution
  • Regular variation
  • Tail dependence function

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