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April 1999 Estimating a tail exponent by modelling departure from a Pareto distribution
Andrey Feuerverger, Peter Hall
Ann. Statist. 27(2): 760-781 (April 1999). DOI: 10.1214/aos/1018031215

Abstract

We suggest two semiparametric methods for accommodating departures from a Pareto model when estimating a tail exponent by fitting the model to extreme-value data. The methods are based on approximate likelihood and on least squares, respectively. The latter is somewhat simpler to use and more robust against departures from classical extreme-value approximations, but produces estimators with approximately 64% greater variance when conventional extreme-value approximations are appropriate. Relative to the conventional assumption that the sampling population has exactly a Pareto distribution beyond a threshold, our methods reduce bias by an order of magnitude without inflating the order of variance. They are motivated by data on extrema of community sizes and are illustrated by an application in that context.

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Andrey Feuerverger. Peter Hall. "Estimating a tail exponent by modelling departure from a Pareto distribution." Ann. Statist. 27 (2) 760 - 781, April 1999. https://doi.org/10.1214/aos/1018031215

Information

Published: April 1999
First available in Project Euclid: 5 April 2002

zbMATH: 0942.62059
MathSciNet: MR1714709
Digital Object Identifier: 10.1214/aos/1018031215

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 2 • April 1999
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