The Annals of Statistics

A Moment Estimator for the Index of an Extreme-Value Distribution

A. L. M. Dekkers, J. H. J. Einmahl, and L. De Haan

Full-text: Open access

Abstract

We extend Hill's well-known estimator for the index of a distribution function with regularly varying tail to an estimate for the index of an extreme-value distribution. Consistency and asymptotic normality are proved. The estimator is used for high quantile and endpoint estimation.

Article information

Source
Ann. Statist. Volume 17, Number 4 (1989), 1833-1855.

Dates
First available: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176347397

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176347397

Mathematical Reviews number (MathSciNet)
MR1026315

Zentralblatt MATH identifier
0701.62029

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62G30: Order statistics; empirical distribution functions

Keywords
Extreme-value theory parameter estimation

Citation

Dekkers, A. L. M.; Einmahl, J. H. J.; Haan, L. De. A Moment Estimator for the Index of an Extreme-Value Distribution. The Annals of Statistics 17 (1989), no. 4, 1833--1855. doi:10.1214/aos/1176347397. http://projecteuclid.org/euclid.aos/1176347397.


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