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Iterative Estimation of the Extreme Value Index

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Abstract

Let {X n , n ≥ 1} be a sequence of independent random variables with common continuous distribution function F having finite and unknown upper endpoint. A new iterative estimation procedure for the extreme value index γ is proposed and one implemented iterative estimator is investigated in detail, which is asymptotically as good as the uniform minimum varianced unbiased estimator in an ideal model. Moreover, the superiority of the iterative estimator over its non iterated counterpart in the non asymptotic case is shown in a simulation study.

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Authors and Affiliations

  1. Department of Mathematical Statistics and Actuarial Science, University of Bern, 3012, Bern, Switzerland

    Samuel Müller & Jürg Hüsler

Authors
  1. Samuel Müller
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  2. Jürg Hüsler
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Correspondence to Samuel Müller.

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AMS 2000 Subject Classification: 62G32

Supported by Swiss National Science foundation.

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Müller, S., Hüsler, J. Iterative Estimation of the Extreme Value Index. Methodol Comput Appl Probab 7, 139–148 (2005). https://doi.org/10.1007/s11009-005-1487-x

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  • DOI: https://doi.org/10.1007/s11009-005-1487-x

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