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Iterative Estimation of the Extreme Value Index

  • Samuel Müller
  • Jürg Hüsler
Article

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.

Keywords

extreme value theory tail index estimation iterative estimator 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Mathematical Statistics and Actuarial ScienceUniversity of BernBernSwitzerland

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