Extreme quantile estimation in [delta]-neighborhoods of generalized Pareto distributions

Michael Falk

Statistics & Probability Letters, 1994, vol. 20, issue 1, 9-21

Abstract: Suppose that we are given an i.i.d. sample of size n from a distribution function F, which lies in a certain neigborhood of a generalized Pareto distribution. A suitable data transformation then reduces the estimation of extreme quantiles of F i.e., quantiles outside the range of our data, to the problem of estimating the location and scale parameter in the family of exponential distributions. We establish bounds for this statistical model reduction, define the pertaining UMVU estimators and discuss their asymptotic behavior.

Keywords: Extreme; value; distribution; Generalized; Pareto; distribution; Large; quantiles; UMVU; estimators; Pickands; estimator (search for similar items in EconPapers)
Date: 1994
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