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

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

Authors: Yahia Djabrane, Zahnit Abida, Brahimi Brahim

Journal: Pakistan Journal of Statistics and Operation Research

HEC Recognition History
Category From To
Y 2020-07-01 2021-06-30

Publisher: Asiatic Region

Country: Pakistan

Year: 2021

Volume: 17

Issue: 1

Language: English

DOI: 10.18187/pjsor.v17i1.2735

Keywords: Extreme value indexExtreme quantilesRandom right-truncationRobust estimationSmall sample

Categories
Extreme Value Theory (15) Risk Management (1217) Data Analysis (701) Statistics (8857) Actuarial Science (96)

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 nite sample behavior of the proposed estimator.  Extreme quantiles estimation is also derived and applied to real data-set of lifetimes of automobile brake pads.

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