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The harmonic moment tail index estimator: asymptotic distribution and robustness

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  • Jan Beran
  • Dieter Schell
  • Milan Stehlík

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. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:1:p:193-220
    DOI: 10.1007/s10463-013-0412-2
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    References listed on IDEAS

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    1. Beran, Jan & Schell, Dieter, 2012. "On robust tail index estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3430-3443.
    2. Vytaras Brazauskas & Robert Serfling, 2000. "Robust and Efficient Estimation of the Tail Index of a Single-Parameter Pareto Distribution," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(4), pages 12-27.
    3. 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.
    4. L. De Haan & L. Peng, 1998. "Comparison of tail index estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(1), pages 60-70, March.
    5. Ana Ferreira & Casper G. de Vries, 2004. "Optimal Confidence Intervals for the Tail Index and High Quantiles," Tinbergen Institute Discussion Papers 04-090/2, Tinbergen Institute.
    6. Mark Finkelstein & Howard G. Tucker & Jerry Alan Veeh, 2006. "Pareto Tail Index Estimation Revisited," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(1), pages 1-10.
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    Cited by:

    1. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    2. Ivanilda Cabral & Frederico Caeiro & M. Ivette Gomes, 2022. "On the comparison of several classical estimators of the extreme value index," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(1), pages 179-196, January.
    3. M. Ivette Gomes & Armelle Guillou, 2015. "Extreme Value Theory and Statistics of Univariate Extremes: A Review," International Statistical Review, International Statistical Institute, vol. 83(2), pages 263-292, August.
    4. Vygantas Paulauskas & Marijus Vaičiulis, 2017. "A class of new tail index estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 461-487, April.
    5. H. M. Barakat & E. M. Nigm & O. M. Khaled & H. A. Alaswed, 2018. "The estimations under power normalization for the tail index, with comparison," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 431-454, July.
    6. Lígia Henriques-Rodrigues & Frederico Caeiro & M. Ivette Gomes, 2024. "A New Class of Reduced-Bias Generalized Hill Estimators," Mathematics, MDPI, vol. 12(18), pages 1-18, September.
    7. Xiao Wang & Lihong Wang, 2024. "A tail index estimation for long memory processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(8), pages 947-971, November.
    8. David J. Hand, 2018. "Statistical challenges of administrative and transaction data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(3), pages 555-605, June.
    9. Emanuele Taufer & Flavio Santi & Pier Luigi Novi Inverardi & Giuseppe Espa & Maria Michela Dickson, 2020. "Extreme Value Index Estimation by Means of an Inequality Curve," Mathematics, MDPI, vol. 8(10), pages 1-17, October.

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