Por Jan Beirlant (Catholic University of Leuven - Belgium).

The subject of tail estimation for randomly censored data from a heavy tailed distribution is motivated by applications for instance in actuarial statistics. The bias of the available estimators of the extreme value index can be substantial and depends strongly on the amount of censoring.  We review the available estimators, propose a new bias reduced estimator, and show how shrinkage estimation can help to keep the MSE under control. We compare these new proposals with the existing estimators through simulation.  A detailed study of a long-tailed car insurance portfolio is presented.