Abstract

The estimation of the extreme value index (EVI) is a fundamental problem in extreme value statistics, as it plays a key role in the analysis of tail behavior and in the assessment of risks associated with rare and severe events. In heavy-tailed models, where the EVI is positive, Hill-type estimators are among the most widely used methods. However, these estimators are often affected by substantial bias, which may reduce the accuracy of inference, particularly in finite samples.
This work focuses on bias reduction frameworks for classes of generalized Hill estimators. The main goal is to improve EVI estimation in heavy-tailed settings by constructing reduced-bias alternatives within flexible generalized Hill families already proposed in the literature. These frameworks allow a systematic comparison of different estimators, both from a methodological perspective and in terms of finite-sample performance.
Special emphasis is given to applications involving environmental data, where accurate modeling of extreme observations is essential. Environmental phenomena such as very high pollution levels, extreme rainfall, heatwaves, droughts, and other climate-related events often exhibit tail features that require appropriate extreme value methods. In such contexts, biased estimation of the EVI may have a direct impact on the evaluation of extreme quantiles, return levels, and risk measures used to support environmental monitoring and decision-making.
The practical relevance of the proposed frameworks is illustrated through the analysis of environmental data sets, showing how bias reduction can improve the stability and credibility of tail inference in applied problems. Overall, this study reinforces the importance of developing flexible and effective bias-correction strategies for generalized Hill estimators, while also emphasizing their value in environmental applications where reliable assessment of extreme risk is of major importance.