A New Class of Reduced-Bias Generalized Hill Estimators

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