Bias correction in multivariate extremes
Résumé
The estimation of the extremal dependence structure is spoiled by the impact of the bias, which increases with the number of ob- servations used for the estimation. Already known in the univariate setting, the bias correction procedure is studied in this paper under the multivariate framework. New families of estimators of the stable tail dependence function are obtained. They are asymptotically unbi- ased versions of the empirical estimator introduced by Huang (1992). Since the new estimators have a regular behaviour with respect to the number of observations, it is possible to deduce aggregated ver- sions so that the choice of the threshold is substantially simplified. An extensive simulation study is provided as well as an application on real data.
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