Speaker
Description
In extreme value theory (EVT), estimating the tail index of heavy-tailed distributions is crucial for understanding rare and extreme events. Traditional estimators such as the Hill and Maximum Likelihood Estimators (MLE) perform well with large samples but struggle
with small sample sizes due to increased bias and variance. In this paper, we introduce a novel estimation technique the Maximum Lq-Likelihood Estimator (MLqE), which incorporates a distortion parameter q, making it more robust to extreme observations and more accurate in small-sample scenarios. We demonstrate that the MLqE is consistent and asymptotically normal, outperforming the classical MLE in terms of mean squared error in
moderate and small sample sizes. Moreover, we present simulation results that highlight the superior performance of the MLqE, particularly when comparing it to the MLE in tail
index estimation. This method not only offers a significant improvement in the accuracy of heavy-tailed distribution parameter estimation but also provides a versatile tool for various
real-world applications, including finance, hydrology, and risk management.
