Asymptotically Unbiased Estimation of the Coefficient of Tail Dependence
Résumé
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.
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