Abstract
In this article, and in a context of regularly varying tails, we suggest a simple generalization of the classical Hill estimator of a positive tail index γ. Such an estimator is merely the Hill estimator associated to artificially shifted data. The shift a imposed to the data is the tuning parameter of the statistical procedure of estimation. Such a tuning parameter enables us, in a great diversity of situations, to reduce the main component of the bias of Hill's estimator, getting thus estimates with stable sample paths around the target value γ, and with small mean squared error.
Acknowledgment
This research was partially supported by FCT/POCTI/FEDER.