Extreme quantile estimation in \(\delta\)-neighborhoods of generalized Pareto distributions
Suppose that a finite sample is available from a population with a distribution function \(F\) which lies in a certain neighborhood of a generalized Pareto distribution. Employing a suitable data transformation one can reduce the estimation of extreme quantiles of \(F\) (i.e. quantiles outside the range of the available data) to the problem of estimating the location and scale parameters in the family of exponential distributions. Bounds for this statistical model reduction are established, the pertaining UMVU estimators are defined and their asymptotic behavior is discussed.
scientific article; zbMATH DE number 633669
scientific article