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Robust Estimation of the Tail Index of a Single Parameter Pareto Distribution from Grouped Data

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  • Chudamani Poudyal

Abstract

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.

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  • Chudamani Poudyal, 2024. "Robust Estimation of the Tail Index of a Single Parameter Pareto Distribution from Grouped Data," Papers 2401.14593, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2401.14593
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    References listed on IDEAS

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    1. Zhao, Qian & Brazauskas, Vytaras & Ghorai, Jugal, 2018. "Robust And Efficient Fitting Of Severity Models And The Method Of Winsorized Moments," ASTIN Bulletin, Cambridge University Press, vol. 48(1), pages 275-309, January.
    2. Nan Lin & Xuming He, 2006. "Robust and efficient estimation under data grouping," Biometrika, Biometrika Trust, vol. 93(1), pages 99-112, March.
    3. Stéphane Guerrier & Elise Dupuis-Lozeron & Yanyuan Ma & Maria-Pia Victoria-Feser, 2019. "Simulation-Based Bias Correction Methods for Complex Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 146-157, January.
    4. Poudyal, Chudamani, 2021. "Robust Estimation Of Loss Models For Lognormal Insurance Payment Severity Data," ASTIN Bulletin, Cambridge University Press, vol. 51(2), pages 475-507, May.
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