Lehmer's mean-of-order-p extreme value index estimation: a simulation study and applications

Area of Science:

• Statistics
• Extreme Value Theory
• Probability

Background:

• Extreme Value Theory (EVT) focuses on estimating extreme event quantities.
• A key challenge in EVT is estimating the extreme value index (EVI), which indicates tail weight.
• Semi-parametric estimation of EVI for heavy tails is crucial for risk assessment.

Purpose of the Study:

• To investigate a novel class of EVI estimators based on Lehmer's mean-of-order (Lp).
• To evaluate the performance of these estimators through large-scale Monte Carlo simulations.
• To explore adaptive and stability-based methods for selecting estimation parameters.

Main Methods:

• Utilized Lehmer's mean-of-order (Lp) as a generalized mean for EVI estimation.
• Conducted extensive Monte Carlo simulations to assess estimator behavior with varying 'p'.
• Developed and applied bootstrap adaptive and stability-based algorithms for parameter selection.

Main Results:

• Demonstrated the competitiveness of Lp-based EVI estimators.
• Showcased the performance of Lp estimators as a function of the parameter 'p'.
• Successfully applied the developed algorithms to both simulated and real-world data.

Conclusions:

• Lehmer's mean-of-order provides a viable approach for semi-parametric EVI estimation in heavy-tailed distributions.
• Adaptive and stability-based methods enhance the practical application of these estimators.
• The findings contribute to more accurate modeling of extreme events.