Estimating a tail exponent by modelling departure from a Pareto distribution

Andrey Feuerverger, Peter Hall

    Research output: Contribution to journalArticlepeer-review

    172 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)760-781
    Number of pages22
    JournalAnnals of Statistics
    Volume27
    Issue number2
    Publication statusPublished - Apr 1999

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