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A Test for Comparing Tail Indices for Heavy-Tailed Distributions via Empirical Likelihood

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  • Julien Worms
  • Rym Worms

Abstract

In this work, the problem of testing whether different (⩾2) independent samples, with (possibly) different heavy-tailed distributions, share the same extreme value index, is addressed. The test statistic proposed is inspired by the empirical likelihood methodology and consists in an ANOVA-like confrontation of Hill estimators. Asymptotic validity of this simple procedure is proved and efficiency, in terms of empirical type I error and power, is investigated through simulations under a variety of situations. Surprisingly, this topic had hardly been addressed before, and only in the two-sample case, though it can prove useful in applications.

Suggested Citation

  • Julien Worms & Rym Worms, 2015. "A Test for Comparing Tail Indices for Heavy-Tailed Distributions via Empirical Likelihood," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(15), pages 3289-3302, August.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:15:p:3289-3302
    DOI: 10.1080/03610926.2013.823204
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    Cited by:

    1. Aigner, Maximilian & Chavez-Demoulin, Valérie & Guillou, Armelle, 2022. "Measuring and comparing risks of different types," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 1-21.

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