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On robust tail index estimation

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  • Beran, Jan
  • Schell, Dieter

Abstract

A new approach to tail index estimation based on huberization of the Pareto MLE is considered. The proposed estimator is robust in a nonstandard way in that it protects against deviations from the central model at low quantiles. Asymptotic normality with the parametric n-rate of convergence is obtained with a bounded asymptotic bias under deviations from the Pareto model. The method is particularly useful for small samples where Hill-type estimators tend to be highly volatile. This is illustrated by a simulation study with sample sizes n≤100.

Suggested Citation

  • Beran, Jan & Schell, Dieter, 2012. "On robust tail index estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3430-3443.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:11:p:3430-3443
    DOI: 10.1016/j.csda.2010.05.028
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    References listed on IDEAS

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    8. Vandewalle, B. & Beirlant, J. & Christmann, A. & Hubert, M., 2007. "A robust estimator for the tail index of Pareto-type distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6252-6268, August.
    9. Berkes, István & Horváth, Lajos & Kokoszka, Piotr, 2003. "Estimation Of The Maximal Moment Exponent Of A Garch(1,1) Sequence," Econometric Theory, Cambridge University Press, vol. 19(4), pages 565-586, August.
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    Cited by:

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    4. Jan Beran & Dieter Schell & Milan Stehlík, 2014. "The harmonic moment tail index estimator: asymptotic distribution and robustness," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 193-220, February.
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    7. Michał Brzeziński, 2013. "Robust estimation of the Pareto index: A Monte Carlo Analysis," Working Papers 2013-32, Faculty of Economic Sciences, University of Warsaw.

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