Extreme quantile estimation in \(\delta\)-neighborhoods of generalized Pareto distributions
type: Item
instance of: scholarly article
title: Extreme quantile estimation in \(\delta\)-neighborhoods of generalized Pareto distributions
zbMATH Open document ID: 0804.62025
DOI: 10.1016/0167-7152(94)90229-1
author: Michael Falk
published in: Statistics \& Probability Letters
publication date: 1995-01-17T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 633669
zbMATH Keywords: bounds
zbMATH Keywords: finite sample
zbMATH Keywords: generalized Pareto distribution
zbMATH Keywords: data transformation
zbMATH Keywords: estimation of extreme quantiles
zbMATH Keywords: location
zbMATH Keywords: scale
zbMATH Keywords: exponential distributions
zbMATH Keywords: model reduction
zbMATH Keywords: UMVU estimators
reviewed by: Joseph Melamed
MaRDI profile type: Publication
full work available at URL: 0167-7152(94)90229-1
OpenAlex ID: W1979127653
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description: scientific article; zbMATH DE number 633669