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June, 1985 On Asymptotic Normality of Hill's Estimator for the Exponent of Regular Variation
E. Haeusler, J. L. Teugels
Ann. Statist. 13(2): 743-756 (June, 1985). DOI: 10.1214/aos/1176349551

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.

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E. Haeusler. J. L. Teugels. "On Asymptotic Normality of Hill's Estimator for the Exponent of Regular Variation." Ann. Statist. 13 (2) 743 - 756, June, 1985. https://doi.org/10.1214/aos/1176349551

Information

Published: June, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0606.62019
MathSciNet: MR790569
Digital Object Identifier: 10.1214/aos/1176349551

Subjects:
Primary: 62G05
Secondary: 62F12 , 62G30

Keywords: limit theorems , order statistics , Parameter estimation , regular variation

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 2 • June, 1985
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