Partial derivatives and confidence intervals of bivariate tail dependence functions

Liang Peng, Yongcheng Qi

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Bivariate extreme value theory was used to estimate a rare event (see de Haan and de Ronde [1998. Sea and wind: multivariate extremes at work. Extremes 1, 7-45]). This procedure involves estimating a tail dependence function. There are several estimators for the tail dependence function in the literature, but their limiting distributions depend on partial derivatives of the tail dependence function. In this paper smooth estimators are proposed for estimating partial derivatives of bivariate tail dependence functions and their asymptotic distributions are derived as well. A simulation study is conducted to compare different estimators of partial derivatives in terms of both mean squared errors and coverage accuracy of confidence intervals of the bivariate tail dependence function based on these different estimators of partial derivatives.

Original languageEnglish (US)
Pages (from-to)2089-2101
Number of pages13
JournalJournal of Statistical Planning and Inference
Volume137
Issue number7
DOIs
StatePublished - Jul 1 2007

Keywords

  • Bivariate extremes
  • Confidence interval
  • Smooth estimation
  • Spectral measure
  • Tail dependence function

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