Bernoulli

  • Bernoulli
  • Volume 13, Number 1 (2007), 175-194.

Assessing confidence intervals for the tail index by Edgeworth expansions for the Hill estimator

Erich Haeusler and Johan Segers

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Abstract

We establish Edgeworth expansions for the distribution function of the standardized Hill estimator for the reciprocal of the index of regular variation of the tail of a distribution function. The expansions are used to derive expansions for coverage probabilities of confidence intervals for the tail index based on the Hill estimator.

Article information

Source
Bernoulli, Volume 13, Number 1 (2007), 175-194.

Dates
First available in Project Euclid: 30 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1175287728

Digital Object Identifier
doi:10.3150/07-BEJ5175

Mathematical Reviews number (MathSciNet)
MR2307402

Zentralblatt MATH identifier
1111.62045

Keywords
asymptotic normality confidence intervals Edgeworth expansions extreme value index Hill estimator regular variation tail index

Citation

Haeusler, Erich; Segers, Johan. Assessing confidence intervals for the tail index by Edgeworth expansions for the Hill estimator. Bernoulli 13 (2007), no. 1, 175--194. doi:10.3150/07-BEJ5175. https://projecteuclid.org/euclid.bj/1175287728


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