Robust and Smooth Estimation of the Extreme Tail Index via Weighted Minimum Density Power Divergence

2025/07/21 by Saida Mancer, Mancer, Saida, Abdelhakim Necir +3 · 1 citation
Mathematics · Economics, Econometrics and Finance · #Statistical Methods and Inference #Monetary Policy and Economic Impact

paper · pdf · doi:10.48550/arxiv.2507.15744

Abstract

By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These estimators can be viewed as a robust generalization of both weighted least squares and kernel-based tail index estimators. We establish the consistency and asymptotic normality of the proposed class. A simulation study is conducted to assess their finite-sample performance in comparison with existing methods.

Citations

• Tail product-limit process for truncated data with application to extreme value index estimation

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