A New Class of Reduced-Bias Generalized Hill Estimators

Lígia Henriques-Rodrigues (), Frederico Caeiro and M. Ivette Gomes
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Lígia Henriques-Rodrigues: School of Science and Technology and Research Center in Mathematics and Applications (CIMA), University of Évora, 7000-671 Évora, Portugal
Frederico Caeiro: NOVA School of Science and Technology (NOVA FCT) and Center for Mathematics and Applications (CMA), NOVA University Lisbon, 2829-516 Caparica, Portugal
M. Ivette Gomes: Department of Statistics and Operational Research (DEIO), Faculty of Sciences of the University of Lisbon (FCUL) and Centre of Statistics and its Applications (CEAUL), University of Lisbon (ULisboa), 1749-016 Lisbon, Portugal

Mathematics, 2024, vol. 12, issue 18, 1-18

Abstract: The estimation of the extreme value index (EVI) is a crucial task in the field of statistics of extremes, as it provides valuable insights into the tail behavior of a distribution. For models with a Pareto-type tail, the Hill estimator is a popular choice. However, this estimator is susceptible to bias, which can lead to inaccurate estimations of the EVI, impacting the reliability of risk assessments and decision-making processes. This paper introduces a novel reduced-bias generalized Hill estimator, which aims to enhance the accuracy of EVI estimation by mitigating the bias.

Keywords: statistics of extremes; generalized means; reduced-bias estimators; extreme value index; asymptotic properties; Monte Carlo simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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