The Annals of Statistics

On Asymptotic Normality of Hill's Estimator for the Exponent of Regular Variation

E. Haeusler and J. L. Teugels

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Abstract

It is shown that Hill's estimator (1975) for the exponent of regular variation is asymptotically normal if the number $k_n$ of extreme order statistics used to construct it tends to infinity appropriately with the sample size $n.$ As our main result, we derive a general condition which can be used to determine the optimal $k_n$ explicitly, provided that some prior knowledge is available on the underlying distribution function with regularly varying upper tail. This condition is simplified under appropriate assumptions and then applied to several examples.

Article information

Source
Ann. Statist., Volume 13, Number 2 (1985), 743-756.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349551

Digital Object Identifier
doi:10.1214/aos/1176349551

Mathematical Reviews number (MathSciNet)
MR790569

Zentralblatt MATH identifier
0606.62019

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62G30: Order statistics; empirical distribution functions 62F12: Asymptotic properties of estimators

Keywords
Regular variation parameter estimation order statistics limit theorems

Citation

Haeusler, E.; Teugels, J. L. On Asymptotic Normality of Hill's Estimator for the Exponent of Regular Variation. Ann. Statist. 13 (1985), no. 2, 743--756. doi:10.1214/aos/1176349551. https://projecteuclid.org/euclid.aos/1176349551


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