Nelson-Aalen kernel estimator to the tail index of right censored Pareto-type data
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908415035441152 |
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| author | Guesmia, Nour Elhouda Necir, Abdelhakim Meraghni, Djamel |
| author_facet | Guesmia, Nour Elhouda Necir, Abdelhakim Meraghni, Djamel |
| contents | On the basis of Nelson-Aalen product-limit estimator of a randomly censored distribution function, we introduce a kernel estimator to the tail index of right-censored Pareto-like data. Under some regularity assumptions, the consistency and asymptotic normality of the proposed estimator are established. A small simulation study shows that the proposed estimator performs much better, in terms of bias and stability, than the existing ones with, a slight increase in the mean squared error. The results are applied to insurance loss data to illustrate the practical effectiveness of our estimator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09152 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nelson-Aalen kernel estimator to the tail index of right censored Pareto-type data Guesmia, Nour Elhouda Necir, Abdelhakim Meraghni, Djamel Statistics Theory On the basis of Nelson-Aalen product-limit estimator of a randomly censored distribution function, we introduce a kernel estimator to the tail index of right-censored Pareto-like data. Under some regularity assumptions, the consistency and asymptotic normality of the proposed estimator are established. A small simulation study shows that the proposed estimator performs much better, in terms of bias and stability, than the existing ones with, a slight increase in the mean squared error. The results are applied to insurance loss data to illustrate the practical effectiveness of our estimator. |
| title | Nelson-Aalen kernel estimator to the tail index of right censored Pareto-type data |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2505.09152 |