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Fitting Censored and Truncated Regression Data Using the Mixture of Experts Models

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  • Tsz Chai Fung
  • Andrei L. Badescu
  • X. Sheldon Lin

Abstract

The logit-weighted reduced mixture of experts model (LRMoE) is a flexible yet analytically tractable non-linear regression model. Though it has shown usefulness in modeling insurance loss frequencies and severities, model calibration becomes challenging when censored and truncated data are involved, which is common in actuarial practice. In this article, we present an extended expectation–conditional maximization (ECM) algorithm that efficiently fits the LRMoE to random censored and random truncated regression data. The effectiveness of the proposed algorithm is empirically examined through a simulation study. Using real automobile insurance data sets, the usefulness and importance of the proposed algorithm are demonstrated through two actuarial applications: individual claim reserving and deductible ratemaking.

Suggested Citation

  • Tsz Chai Fung & Andrei L. Badescu & X. Sheldon Lin, 2022. "Fitting Censored and Truncated Regression Data Using the Mixture of Experts Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 26(4), pages 496-520, November.
    • Handle: RePEc:taf:uaajxx:v:26:y:2022:i:4:p:496-520
    DOI: 10.1080/10920277.2021.2013896
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    Cited by:

    1. Fung, Tsz Chai, 2022. "Maximum weighted likelihood estimator for robust heavy-tail modelling of finite mixture models," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 180-198.
    2. Spark C. Tseung & Ian Weng Chan & Tsz Chai Fung & Andrei L. Badescu & X. Sheldon Lin, 2023. "Improving risk classification and ratemaking using mixture‐of‐experts models with random effects," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(3), pages 789-820, September.
    3. Sebastian Calcetero-Vanegas & Andrei L. Badescu & X. Sheldon Lin, 2023. "Claim Reserving via Inverse Probability Weighting: A Micro-Level Chain-Ladder Method," Papers 2307.10808, arXiv.org, revised Jun 2024.
    4. Li, Zhengxiao & Wang, Fei & Zhao, Zhengtang, 2024. "A new class of composite GBII regression models with varying threshold for modeling heavy-tailed data," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 45-66.

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