  The subject of tail estimation for randomly censored data from a heavy tailed
distribution receives growing attention, 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. A
bootstrap algorithm is proposed to construct confidence intervals. We compare
these new proposals with the existing estimators through simulation. We
conclude this paper with a detailed study of a long-tailed car insurance
portfolio, which typically exhibit heavy censoring.
