Estimating the end-point of a probability distribution using minimum-distance methods
Date
1999
Authors
Hall, Peter
Wang, Jane-Ling
Journal Title
Journal ISSN
Volume Title
Publisher
Chapman & Hall
Abstract
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 maximumlikelihood 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.
Description
Keywords
Keywords: 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
Citation
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Source
Bernoulli
Type
Journal article