Bernoulli

  • Bernoulli
  • Volume 14, Number 4 (2008), 1003-1026.

A method of moments estimator of tail dependence

John H.J. Einmahl, Andrea Krajina, and Johan Segers

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Abstract

In the world of multivariate extremes, estimation of the dependence structure still presents a challenge and an interesting problem. A procedure for the bivariate case is presented that opens the road to a similar way of handling the problem in a truly multivariate setting. We consider a semi-parametric model in which the stable tail dependence function is parametrically modeled. Given a random sample from a bivariate distribution function, the problem is to estimate the unknown parameter. A method of moments estimator is proposed where a certain integral of a nonparametric, rank-based estimator of the stable tail dependence function is matched with the corresponding parametric version. Under very weak conditions, the estimator is shown to be consistent and asymptotically normal. Moreover, a comparison between the parametric and nonparametric estimators leads to a goodness-of-fit test for the semiparametric model. The performance of the estimator is illustrated for a discrete spectral measure that arises in a factor-type model and for which likelihood-based methods break down. A second example is that of a family of stable tail dependence functions of certain meta-elliptical distributions.

Article information

Source
Bernoulli, Volume 14, Number 4 (2008), 1003-1026.

Dates
First available in Project Euclid: 6 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.bj/1225980569

Digital Object Identifier
doi:10.3150/08-BEJ130

Mathematical Reviews number (MathSciNet)
MR2543584

Zentralblatt MATH identifier
1155.62017

Keywords
asymptotic properties confidence regions goodness-of-fit test meta-elliptical distribution method of moments multivariate extremes tail dependence

Citation

Einmahl, John H.J.; Krajina, Andrea; Segers, Johan. A method of moments estimator of tail dependence. Bernoulli 14 (2008), no. 4, 1003--1026. doi:10.3150/08-BEJ130. https://projecteuclid.org/euclid.bj/1225980569


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