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

Julien Worms and Rym Worms

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 15, 3289-3302

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.

Date: 2015
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DOI: 10.1080/03610926.2013.823204

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