Asymptotically Unbiased Estimation of the Coefficient of Tail Dependence

Yuri Goegebeur (1) , Armelle Guillou (2)

1 IMADA - Department of Mathematics and Computer Science [Odense]
2 IRMA - Institut de Recherche Mathématique Avancée

We introduce and study a class of weighted functional estimators for the coefficient of tail dependence in bivariate extreme value statistics. Asymptotic normality of these estimators is established under a second-order condition on the joint tail behaviour, some conditions on the weight function and for appropriately chosen sequences of intermediate order statistics. Asymptot-ically unbiased estimators are constructed by judiciously chosen linear combinations of weighted functional estimators, and variance optimality within this class of asymptotically unbiased esti-mators is discussed. The finite sample performance of some specific examples from our class of estimators and some alternatives from the recent literature are evaluated with a small simulation experiment.

Mots clés: bias-correction; coefficient of tail dependence; multivariate extremes; second-order condition

Domaines: Statistiques [math.ST]

Yuri Goegebeur, Armelle Guillou. Asymptotically Unbiased Estimation of the Coefficient of Tail Dependence. Scandinavian Journal of Statistics, 2013, 40 (1), ⟨10.1111/j.1467-9469.2012.00800.x⟩. ⟨hal-01311656⟩