On robust tail index extimation under incomplete data

Abstract

In this thesis, we propose a new robust estimation procedure for the tail index for Pareto-type distributions under incomplete data (censorship or truncation). Under truncation, the extreme quantile estimation is also derived and applied to an actual data set on automobile brake pad life. Simulation study using R statistical software is carried out to evaluate the performance and the robustness of the proposed estimators for small and large sample size and for both uncontaminated and contaminated cases. Our newly estimators have been shown to be more robust and perform better than existing Hill-type estimators based on upper order statistics, in both cases of incomplete data (censorshipor truncation)