The Annals of Statistics

On the Estimation of the Extreme-Value Index and Large Quantile Estimation

Arnold L. M. Dekkers and Laurens De Haan

Full-text: Open access

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.

Article information

Source
Ann. Statist. Volume 17, Number 4 (1989), 1795-1832.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347396

Digital Object Identifier
doi:10.1214/aos/1176347396

Mathematical Reviews number (MathSciNet)
MR1026314

Zentralblatt MATH identifier
0699.62028

JSTOR
links.jstor.org

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

Keywords
Extreme-value theory order statistics strong consistency asymptotic normality

Citation

Dekkers, Arnold L. M.; Haan, Laurens De. On the Estimation of the Extreme-Value Index and Large Quantile Estimation. Ann. Statist. 17 (1989), no. 4, 1795--1832. doi:10.1214/aos/1176347396. https://projecteuclid.org/euclid.aos/1176347396.


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