Estimating the End-Point of a Probability Distribution Using Minimum-Distance Methods

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.