A technique based on minimum distance, derived from a coefficient of determination and representable in terms of Greenwood's statistic, is used to derive an estimator of the end-point of a distribution. It is appropriate in cases where the actual sample size is very large and perhaps unknown. The minimum-distance estimator is compared with a competitor based on maximum likelihood and shown to enjoy lower asymptotic variance for a range of values of the extremal exponent. When only a small number of extremes is available, it is well defined much more frequently than the maximum-likelihood estimator. The minimum-distance method allows exact interval estimation, since the version of Greenwood's statistic on which it is based does not depend on nuisance parameters.
Publié le : 1999-02-14
Classification:
central limit theorem,
coefficient of determination,
domain of attraction,
extreme value theory,
goodness of fit,
Greenwood's statistic,
least-squares maximum-likelihood order statistic,
Pareto distribution,
sporting records,
Weibull distribution
@article{1173707100,
author = {Hall, Peter and Wang, Julian Z.},
title = {Estimating the end-point of a probability distribution using minimum-distance methods},
journal = {Bernoulli},
volume = {5},
number = {6},
year = {1999},
pages = { 177-189},
language = {en},
url = {http://dml.mathdoc.fr/item/1173707100}
}
Hall, Peter; Wang, Julian Z. Estimating the end-point of a probability distribution using minimum-distance methods. Bernoulli, Tome 5 (1999) no. 6, pp. 177-189. http://gdmltest.u-ga.fr/item/1173707100/