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

Trimmed extreme value estimators for censored heavy-tailed data