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The harmonic moment tail index estimator: asymptotic distribution and robustness

Abstract

Asymptotic properties of the harmonic moment tail index Estimator are derived for distributions with regularly varying tails. The estimator shows good robustness properties and stands out for its simplicity. A tuning parameter allows for regulating the trade-off between robustness and efficiency. Small sample properties are illustrated by a simulation study.

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Acknowledgments

We would like to thank a referee and the associate editor for their constructive remarks that led to an improved presentation of the results. This research has been supported by the DFG (grant BE 2123/10-1).

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Correspondence to Jan Beran.

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Beran, J., Schell, D. & Stehlík, M. The harmonic moment tail index estimator: asymptotic distribution and robustness. Ann Inst Stat Math 66, 193–220 (2014). https://doi.org/10.1007/s10463-013-0412-2

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  • DOI: https://doi.org/10.1007/s10463-013-0412-2

Keywords

  • Tail index estimation
  • Regularly varying tail
  • Hill estimator
  • Robustness
  • Asymptotic distribution