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Penultimate Approximation for Hill's Estimator

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  • S. Cheng
  • L. De Haan

Abstract

We prove that the probability distribution of Hill's estimator can be better approximated by a series of appropriate gamma distributions than by the limiting normal distribution.

Suggested Citation

  • S. Cheng & L. De Haan, 2001. "Penultimate Approximation for Hill's Estimator," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 569-575, September.
    • Handle: RePEc:bla:scjsta:v:28:y:2001:i:3:p:569-575
    DOI: 10.1111/1467-9469.00255
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    Cited by:

    1. Haeusler, E. & Segers, J., 2005. "Assessing Confidence Intervals for the Tail Index by Edgeworth Expansions for the Hill Estimator," Discussion Paper 2005-129, Tilburg University, Center for Economic Research.
    2. Cuntz, A. & Haeusler, E. & Segers, J.J.J., 2003. "Edgeworth Expansions for the Distribution Function of the Hill Estimator," Other publications TiSEM 345501c7-c622-4b04-8d27-9, Tilburg University, School of Economics and Management.
    3. Haeusler, E. & Segers, J., 2005. "Assessing Confidence Intervals for the Tail Index by Edgeworth Expansions for the Hill Estimator," Other publications TiSEM e635c476-8fa8-4f16-8760-2, Tilburg University, School of Economics and Management.
    4. Cuntz, A. & Haeusler, E. & Segers, J.J.J., 2003. "Edgeworth Expansions for the Distribution Function of the Hill Estimator," Discussion Paper 2003-8, Tilburg University, Center for Economic Research.

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