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A class of new tail index estimators

Author

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  • Vygantas Paulauskas

    (Vilnius University)

  • Marijus Vaičiulis

    (Vilnius University)

Abstract

In the paper, we propose a new class of functions which is used to construct tail index estimators. Functions from this new class are non-monotone in general, but they are the product of two monotone functions: the power function and the logarithmic function, which play essential role in the classical Hill estimator. The newly introduced generalized moment ratio estimator and generalized Hill estimator have a better asymptotic performance compared with the corresponding classical estimators over the whole range of the parameters that appear in the second-order regular variation condition. Asymptotic normality of the introduced estimators is proved, and comparison (using asymptotic mean square error) with other estimators of the tail index is provided. Some preliminary simulation results are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:2:d:10.1007_s10463-015-0548-3
    DOI: 10.1007/s10463-015-0548-3
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    References listed on IDEAS

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    1. Gomes, M. Ivette & Pestana, Dinis & Caeiro, Frederico, 2009. "A note on the asymptotic variance at optimal levels of a bias-corrected Hill estimator," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 295-303, February.
    2. Fátima Brilhante, M. & Ivette Gomes, M. & Pestana, Dinis, 2013. "A simple generalisation of the Hill estimator," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 518-535.
    3. 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.
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    7. 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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    Cited by:

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    3. 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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