Robust estimation of the extreme value index of Pareto-type distributions under random truncation with applications

Abstract

In this paper, we introduce a new robust estimator for the extreme value index of Pareto-type distributions under randomly right-truncated data and establish its consistency and asymptotic normality. Our considerations are based on the Lynden-Bell integral and a useful huberized M-functional and M-estimators of the tail index. A simulation study is carried out to evaluate the robustness and the finite sample behavior of the proposed estimator. Moreover, an extreme quantiles estimation was also derived and applied to real data-set of lifetimes of automobile brake pads.