Open Access
2021 Trimmed extreme value estimators for censored heavy-tailed data
Martin Bladt, Hansjörg Albrecher, Jan Beirlant
Author Affiliations +
Electron. J. Statist. 15(1): 3112-3136 (2021). DOI: 10.1214/21-EJS1857


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.

Funding Statement

The authors acknowledge financial support from the Swiss National Science Foundation Project 200021_191984.


Download Citation

Martin Bladt. Hansjörg Albrecher. Jan Beirlant. "Trimmed extreme value estimators for censored heavy-tailed data." Electron. J. Statist. 15 (1) 3112 - 3136, 2021.


Received: 1 January 2021; Published: 2021
First available in Project Euclid: 8 June 2021

Digital Object Identifier: 10.1214/21-EJS1857

Keywords: Asymptotic distributions , Heavy-tailed estimation , Right-censored data

Vol.15 • No. 1 • 2021
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