Trimmed extreme value estimators for censored heavy-tailed data

Abstract

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.

Distributed Trimmed Hill Estimator

“…A number of reseachers also considered trimming but of the models rather than the data, see [9] and [10]. Moreover, the random censoring for heavy-tailed distribution was discussed in [11] [12] [13] and [14]. Contrary to the above, here we assume to have non-truncated heavy-tailed model and only the top order statistics are contaminated in the associated data.…”