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A class of new tail index estimators

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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.

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Acknowledgments

The authors are grateful to anonymous referees and the editor whose remarks and suggestions were very helpful in improving the paper.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Vilnius University, Naugarduko st. 24, 03225, Vilnius, Lithuania

    Vygantas Paulauskas

  2. Institute of Mathematics and Informatics, Vilnius University, Akademijos st. 4, 08663, Vilnius, Lithuania

    Marijus Vaičiulis

Authors
  1. Vygantas Paulauskas
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  2. Marijus Vaičiulis
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Corresponding author

Correspondence to Vygantas Paulauskas.

Additional information

The research was supported by Research Council of Lithuania, Grant No. MIP-076/2013.

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Paulauskas, V., Vaičiulis, M. A class of new tail index estimators. Ann Inst Stat Math 69, 461–487 (2017). https://doi.org/10.1007/s10463-015-0548-3

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  • DOI: https://doi.org/10.1007/s10463-015-0548-3

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