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Truncated Estimation of Ratio Statistics with Application to Heavy Tail Distributions

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Abstract

The problem of estimation of the heavy tail index is revisited from the point of view of truncated estimation. A class of novel estimators is introduced having guaranteed accuracy based on a sample of fixed size. The performance of these estimators is quantified both theoretically and in simulations over a host of relevant examples. It is also shown that in several cases the proposed estimators attain — within a logarithmic factor — the optimal parametric rate of convergence. The property of uniform asymptotic normality of the proposed estimators is established.

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Authors and Affiliations

  1. Dept. Math., Univ. of California, San Diego, USA

    D. N. Politis

  2. Dept. Appl.Math. and Cybern., Tomsk State University, Tomsk, Russia

    V. A. Vasiliev & S. E. Vorobeychikov

Authors
  1. D. N. Politis
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  2. V. A. Vasiliev
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  3. S. E. Vorobeychikov
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Correspondence to D. N. Politis.

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Politis, D.N., Vasiliev, V.A. & Vorobeychikov, S.E. Truncated Estimation of Ratio Statistics with Application to Heavy Tail Distributions. Math. Meth. Stat. 27, 226–243 (2018). https://doi.org/10.3103/S1066530718030043

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  • DOI: https://doi.org/10.3103/S1066530718030043

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