Open Access
June, 1982 On Estimating the Endpoint of a Distribution
Peter Hall
Ann. Statist. 10(2): 556-568 (June, 1982). DOI: 10.1214/aos/1176345796


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.


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Peter Hall. "On Estimating the Endpoint of a Distribution." Ann. Statist. 10 (2) 556 - 568, June, 1982.


Published: June, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0489.62029
MathSciNet: MR653530
Digital Object Identifier: 10.1214/aos/1176345796

Primary: 62F10
Secondary: 60F05 , 62G05

Keywords: central limit theorem , efficiency , endpoint , Extreme order statistics , regularly varying , robust

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • June, 1982
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