A test for comparing tail indices for heavy-tailed distributions via empirical likelihood

Julien Worms (1) , Rym Worms (2)

1 LMV - Laboratoire de Mathématiques de Versailles
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

In this work, the problem of testing whether different ($\geq 2$) 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.

Mots clés: Empirical Likelihood; Extreme values; Tail index; Comparison Test; Hill Estimator; Empirical Likelihood.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Julien Worms, Rym Worms. A test for comparing tail indices for heavy-tailed distributions via empirical likelihood. Communications in Statistics - Theory and Methods, 2015, 44, pp.3289-3302. ⟨10.1080/03610926.2013.823204⟩. ⟨hal-00733240⟩