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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

    (Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA)

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 a 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), pecifically designed to estimate the tail index of a Pareto distribution from grouped data. Inferential justification of the MTuM is established by employing the central limit theorem and validating it through a comprehensive simulation study.

Suggested Citation

  • Chudamani Poudyal, 2024. "Robust Estimation of the Tail Index of a Single Parameter Pareto Distribution from Grouped Data," Risks, MDPI, vol. 12(3), pages 1-13, March.
    • Handle: RePEc:gam:jrisks:v:12:y:2024:i:3:p:45-:d:1349342
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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.
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    1. 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.
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