Paper: arXiv 2401.14593

Authors: 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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a novel robust estimation technique (Method of Truncated Moments) specifically tailored for grouped loss severity data following a Pareto distribution. It provides theoretical asymptotic properties using the Central Limit Theorem and validates the approach through a structured simulation study. While the empirical domain is primarily simulation-focused rather than backtested on live market datasets, the theoretical development is sound and highly relevant for actuarial and tail-risk modeling.

Research Flowchart

  flowchart TD
    A[Goal: Robust Tail Index Estimation for Grouped Pareto Data] --> B[Input: Grouped Loss Severity Data]
    B --> C[Develop Method of Truncated Moments - MTuM]
    C --> D[Apply Central Limit Theorem for Inferential Justification]
    D --> E[Run Comprehensive Simulation Study]
    E --> F[Compare MTuM against MLE & Robust Alternatives]
    F --> G[Outcome: Validated Robust MTuM Estimator for Grouped Data]