The Annals of Statistics

On Estimating the Endpoint of a Distribution

Peter Hall

Full-text: Open access

Abstract

We propose a method of estimating the endpoint, $\theta$, of a distribution when only limited information is available about the behaviour of the distribution in the neighbourhood of $\theta$. By using increasing numbers of extreme order statistics we obtain an estimator which improves on earlier estimators based on only a bounded number of extremes. In a certain particular model our estimator is equal to a maximum likelihood estimator, but it is robust against departures from this model.

Article information

Source
Ann. Statist., Volume 10, Number 2 (1982), 556-568.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345796

Digital Object Identifier
doi:10.1214/aos/1176345796

Mathematical Reviews number (MathSciNet)
MR653530

Zentralblatt MATH identifier
0489.62029

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62G05: Estimation 60F05: Central limit and other weak theorems

Keywords
Central limit theorem efficiency endpoint extreme order statistics regularly varying robust

Citation

Hall, Peter. On Estimating the Endpoint of a Distribution. Ann. Statist. 10 (1982), no. 2, 556--568. doi:10.1214/aos/1176345796. https://projecteuclid.org/euclid.aos/1176345796


Export citation