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Maximum weighted likelihood estimator for robust heavy-tail modelling of finite mixture models

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  • Fung, Tsz Chai

Abstract

Insurance claim severity data are characterized by complex distributional phenomenons, where flexible density estimation tools such as the finite mixture models (FMM) are necessary. However, maximum likelihood estimations (MLE) often produce unstable tail estimates for the FMM. Motivated by this challenge, this article presents a maximum weighted likelihood estimator (MWLE) for robust estimations of heavy-tailed FMM. Under some regularity conditions, the proposed MWLE is consistent and asymptotically normal. Since the MWLE has a probabilistic interpretation, we are able to develop two distinctive versions of the Generalized Expectation-Maximization (GEM) algorithm to estimate the MWLE parameters more efficiently and reliably than the standard gradient-based algorithms. We apply the proposed MWLE to two simulation studies and a real motor insurance dataset to demonstrate that it better extrapolates the extreme losses than the MLE, without sacrificing the flexibility of the FMM in capturing the small attritional claims.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:107:y:2022:i:c:p:180-198
    DOI: 10.1016/j.insmatheco.2022.08.008
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    More about this item

    Keywords

    Generalized expectation-maximization algorithm; M-estimator; Random truncation; Regularly varying function; Multimodal distribution;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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