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December, 1989 On the Estimation of the Extreme-Value Index and Large Quantile Estimation
Arnold L. M. Dekkers, Laurens De Haan
Ann. Statist. 17(4): 1795-1832 (December, 1989). DOI: 10.1214/aos/1176347396

Abstract

This paper consists of two parts. An easy proof is given for the weak consistency of Pickands' estimate for the main parameter of an extreme-value distribution. Moreover, further natural conditions are given for strong consistency and for asymptotic normality of the estimate. Next a large quantile of a distribution is estimated by a combination of extreme or intermediate order statistics. This leads to an asymptotic confidence interval.

Citation

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Arnold L. M. Dekkers. Laurens De Haan. "On the Estimation of the Extreme-Value Index and Large Quantile Estimation." Ann. Statist. 17 (4) 1795 - 1832, December, 1989. https://doi.org/10.1214/aos/1176347396

Information

Published: December, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0699.62028
MathSciNet: MR1026314
Digital Object Identifier: 10.1214/aos/1176347396

Subjects:
Primary: 62F12
Secondary: 62G30

Keywords: asymptotic normality , extreme-value theory , order statistics , strong consistency

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 4 • December, 1989
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