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Approximation of the Hill estimator process

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  • Kaufmann, E.
  • Reiss, R. -D.

Abstract

An approximation result for a vector of Hill estimators - in the following addressed as Hill process - is proven. It is shown that the Hill process can be approximated on a suitable probability space by a Wiener process and a deterministic bias term. Moreover, the accuracy of the approximation is, roughly speaking, given by the rate of convergence of a certain term in the Karamata representation of the quantile function.

Suggested Citation

  • Kaufmann, E. & Reiss, R. -D., 1998. "Approximation of the Hill estimator process," Statistics & Probability Letters, Elsevier, vol. 39(4), pages 347-354, August.
    • Handle: RePEc:eee:stapro:v:39:y:1998:i:4:p:347-354
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    References listed on IDEAS

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    1. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
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    Cited by:

    1. Holger Drees & Laurens F.M. de Haan & Sidney Resnick, 1998. "How to make a Hill Plot," Tinbergen Institute Discussion Papers 98-090/4, Tinbergen Institute.

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