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Estimation of the tail index for lattice-valued sequences

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Abstract

If one applies the Hill, Pickands or Dekkers–Einmahl–de Haan estimators of the tail index of a distribution to data which are rounded off one often observes that these estimators oscillate strongly as a function of the number k of order statistics involved. We study this phenomenon in the case of a Pareto distribution. We provide formulas for the expected value and variance of the Hill estimator and give bounds on k when the central limit theorem is still applicable. We illustrate the theory by using simulated and real-life data.

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Authors and Affiliations

  1. Department of Business Administration, Nanzan University, 18 Yamazato-cho Showa-ku, Nagoya, 466-8673, Japan

    Muneya Matsui

  2. Department of Mathematics, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark

    Thomas Mikosch

  3. Department of Statistics, College of Sciences, University of Shiraz, Shiraz, 71454, Iran

    Laleh Tafakori

Authors
  1. Muneya Matsui
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  2. Thomas Mikosch
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  3. Laleh Tafakori
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Corresponding author

Correspondence to Muneya Matsui.

Additional information

Thomas Mikosch’s research is partly supported by the Danish Natural Science Research Council (FNU) Grants 09-072331 “Point process modelling and statistical inference” and 10-084172 “Heavy tail phenomena: Modeling and estimation”. Muneya Matsui’s research is partly supported by the JSPS Grant-in-Aid for Research Activity start-up Grant Number 23800065. Parts of this paper were written when Laleh Tafakori and Muneya Matsui were visiting the Department of Mathematics of the University of Copenhagen. They would like to thank for hospitality of the host institution.

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Matsui, M., Mikosch, T. & Tafakori, L. Estimation of the tail index for lattice-valued sequences. Extremes 16, 429–455 (2013). https://doi.org/10.1007/s10687-012-0167-9

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  • DOI: https://doi.org/10.1007/s10687-012-0167-9

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