Robust Estimation of the Tail Index of a Single Parameter Pareto Distribution from Grouped Data
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910338617704448 |
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| author | Poudyal, Chudamani |
| author_facet | Poudyal, Chudamani |
| contents | Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed ground-up loss severity sample dataset is available. However, the options for robust alternatives to MLE become significantly limited when dealing with grouped loss severity data, with only a handful of methods like least squares, minimum Hellinger distance, and optimal bounded influence function available. This paper introduces a novel robust estimation technique, the Method of Truncated Moments (MTuM), specifically designed to estimate the tail index of a Pareto distribution from grouped data. Inferential justification of MTuM is established by employing the central limit theorem and validating them through a comprehensive simulation study. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_14593 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust Estimation of the Tail Index of a Single Parameter Pareto Distribution from Grouped Data Poudyal, Chudamani Methodology Statistics Theory Risk Management Computation Machine Learning 62F35, 62P05 Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed ground-up loss severity sample dataset is available. However, the options for robust alternatives to MLE become significantly limited when dealing with grouped loss severity data, with only a handful of methods like least squares, minimum Hellinger distance, and optimal bounded influence function available. This paper introduces a novel robust estimation technique, the Method of Truncated Moments (MTuM), specifically designed to estimate the tail index of a Pareto distribution from grouped data. Inferential justification of MTuM is established by employing the central limit theorem and validating them through a comprehensive simulation study. |
| title | Robust Estimation of the Tail Index of a Single Parameter Pareto Distribution from Grouped Data |
| topic | Methodology Statistics Theory Risk Management Computation Machine Learning 62F35, 62P05 |
| url | https://arxiv.org/abs/2401.14593 |