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

Chudamani Poudyal

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arXiv · 2401.14593

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

Chudamani Poudyal

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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. 2024-01-26. Robust Estimation of the Tail Index of a Single Parameter Pareto Distribution from Grouped Data. https://arxiv.org/abs/2401.14593

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