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Abelian and Tauberian Theorems on the Bias of the Hill Estimator

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  • JOHAN SEGERS

Abstract

The bias of Hill's estimator for the positive extreme value index of a distribution is investigated in relation to the convergence rate in the regular variation property of the tail function of the common distribution of the sample and the corresponding tail quantile function. Based on the theory of generalized regular variation, natural second‐order conditions are proposed which both imply and are implied by convergence of the expectation of Hill's estimator to the extreme value index at certain rates. A comparison with second‐order conditions encountered in the literature is made.

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  • Johan Segers, 2002. "Abelian and Tauberian Theorems on the Bias of the Hill Estimator," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 461-483, September.
    • Handle: RePEc:bla:scjsta:v:29:y:2002:i:3:p:461-483
    DOI: 10.1111/1467-9469.00301
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    Cited by:

    1. Dufour, Jean-Marie & Kurz-Kim, Jeong-Ryeol, 2010. "Exact inference and optimal invariant estimation for the stability parameter of symmetric [alpha]-stable distributions," Journal of Empirical Finance, Elsevier, vol. 17(2), pages 180-194, March.
    2. Hill, Jonathan B. & Shneyerov, Artyom, 2013. "Are there common values in first-price auctions? A tail-index nonparametric test," Journal of Econometrics, Elsevier, vol. 174(2), pages 144-164.
    3. Jonathan B. Hill & Artyom Shneyerov, 2009. "Are There Common Values in BC Timber Sales? A Tail-Index Nonparametric Test," Working Papers 09003, Concordia University, Department of Economics.

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