On Estimating the Endpoint of a Distribution
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.
Permanent link to this document: http://projecteuclid.org/euclid.aos/1176345796
Digital Object Identifier: doi:10.1214/aos/1176345796
Mathematical Reviews number (MathSciNet): MR653530
Zentralblatt MATH identifier: 0489.62029