The Annals of Statistics

Estimating a tail exponent by modelling departure from a Pareto distribution

Andrey Feuerverger and Peter Hall

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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.

Article information

Source
Ann. Statist., Volume 27, Number 2 (1999), 760-781.

Dates
First available in Project Euclid: 5 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1018031215

Digital Object Identifier
doi:10.1214/aos/1018031215

Mathematical Reviews number (MathSciNet)
MR1714709

Zentralblatt MATH identifier
0942.62059

Keywords
Bias reduction extreme-value theory log-spacings maximum likelihood order statistics peaks-over-threshold regression regular variation spacings Zipf ’s law.

Citation

Feuerverger, Andrey; Hall, Peter. Estimating a tail exponent by modelling departure from a Pareto distribution. Ann. Statist. 27 (1999), no. 2, 760--781. doi:10.1214/aos/1018031215. https://projecteuclid.org/euclid.aos/1018031215


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  • TORONTO, ONTARIO CANBERRA ACT 0200 CANADA M55 3G3 AUSTRALIA E-MAIL: halpstat@pretty.anu.edu.au