Robust and Smooth Estimation of the Extreme Tail Index via Weighted Minimum Density Power Divergence
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| Format: | Preprint |
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2025
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| _version_ | 1866909703071596544 |
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| author | Mancer, Saida Necir, Abdelhakim Meraghni, Djamel |
| author_facet | Mancer, Saida Necir, Abdelhakim Meraghni, Djamel |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_15744 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust and Smooth Estimation of the Extreme Tail Index via Weighted Minimum Density Power Divergence Mancer, Saida Necir, Abdelhakim Meraghni, Djamel Statistics Theory 62G32, 62G05, 62G20, 62G35 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. |
| title | Robust and Smooth Estimation of the Extreme Tail Index via Weighted Minimum Density Power Divergence |
| topic | Statistics Theory 62G32, 62G05, 62G20, 62G35 |
| url | https://arxiv.org/abs/2507.15744 |