  We consider estimation of the extreme value index and extreme quantiles for
heavy-tailed data that are right-censored. We study a general procedure of
removing low importance observations in tail estimators. This trimming
procedure is applied to the state-of-the-art estimators for randomly
right-censored tail estimators. Through an averaging procedure over the amount
of trimming we derive new kernel type estimators. Extensive simulation suggests
that one of the new considered kernels leads to a highly competitive estimator
against virtually any other available alternative in this framework. Moreover,
we propose an adaptive selection method for the amount of top data used in
estimation based on the trimming procedure minimizing the asymptotic mean
squared error. We also provide an illustration of this approach to simulated as
well as to real-world MTPL insurance data.
