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Extremes

, Volume 13, Issue 3, pp 269–290 | Cite as

Asymptotic normality of location invariant heavy tail index estimator

  • Jiaona Li
  • Zuoxiang Peng
  • Saralees Nadarajah
Article

Abstract

Motivated by Fraga Alves (Extremes 4:199–217, 2001)’s work, a new class of location invariant Hill-type estimators for the tail index of a heavy tailed distribution is proposed in the paper. Its asymptotic behavior is derived, and the optimal choice of the sample fraction is discussed by mean squared error. Asymptotic comparisons and simulation studies are presented to show that the new estimator performs well compared to the known ones.

Keywords

Asymptotic normality Location invariant index estimator Second order regular variation Tail index 

AMS 2000 Subject Classifications

Primary—62G32 Secondary—65C05 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsSouthwest UniversityChongqingChina
  2. 2.School of MathematicsUniversity of ManchesterManchesterUK

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