Assessing Confidence Intervals for the Tail Index by Edgeworth Expansions for the Hill Estimator

CentER Discussion Paper No. 2005-129

26 Pages Posted: 17 Jan 2006

See all articles by Erich Haeusler

Erich Haeusler

University of Giessen

Johan Segers

Catholic University of Louvain (UCL)

Date Written: December 2005

Abstract

We establish Edgeworth expansions for the distribution function of the centered and normalized 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.

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

JEL Classification: C13, C14

Suggested Citation

Haeusler, Erich and Segers, Johan, Assessing Confidence Intervals for the Tail Index by Edgeworth Expansions for the Hill Estimator (December 2005). CentER Discussion Paper No. 2005-129, Available at SSRN: https://ssrn.com/abstract=875610 or http://dx.doi.org/10.2139/ssrn.875610

Erich Haeusler (Contact Author)

University of Giessen ( email )

Betriebswirtschaftslehre VII
Giessen, 35394
Germany

Johan Segers

Catholic University of Louvain (UCL) ( email )

Place Montesquieu, 3
Louvain-la-Neuve, 1348
Belgium
+32 10 474311 (Phone)
+32 10 473032 (Fax)

HOME PAGE: http://www.uclouvain.be/stat

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