IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v88y2025i2d10.1007_s00184-024-00952-6.html
   My bibliography  Save this article

Robust estimation and diagnostic of generalized linear model for insurance losses: a weighted likelihood approach

Author

Listed:
  • Tsz Chai Fung

    (Georgia State University)

Abstract

This paper presents a score-based weighted likelihood estimator (SWLE) for robust estimations of the generalized linear model (GLM) for insurance loss data. The SWLE exhibits a limited sensitivity to the outliers, theoretically justifying its robustness against model contaminations. Also, with the specially designed weight function to effectively diminish the contributions of extreme losses to the GLM parameter estimations, most statistical quantities can still be derived analytically, minimizing the computational burden for parameter calibrations. Apart from robust estimations, the SWLE can also act as a quantitative diagnostic tool to detect outliers and systematic model misspecifications. Motivated by the coverage modifications which make insurance losses often random censored and truncated, the SWLE is extended to accommodate censored and truncated data. We exemplify the SWLE on three simulation studies and two real insurance datasets. Empirical results suggest that the SWLE produces more reliable parameter estimates than the MLE if outliers contaminate the dataset. The SWLE diagnostic tool also successfully detects any systematic model misspecifications with high power, accompanying some potential model improvements.

Suggested Citation

  • Tsz Chai Fung, 2025. "Robust estimation and diagnostic of generalized linear model for insurance losses: a weighted likelihood approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(2), pages 149-182, February.
    • Handle: RePEc:spr:metrik:v:88:y:2025:i:2:d:10.1007_s00184-024-00952-6
    DOI: 10.1007/s00184-024-00952-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-024-00952-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-024-00952-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Tsz Chai Fung & George Tzougas & Mario V. Wüthrich, 2023. "Mixture Composite Regression Models with Multi-type Feature Selection," North American Actuarial Journal, Taylor & Francis Journals, vol. 27(2), pages 396-428, April.
    3. 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.
    4. Robert Serfling, 2002. "Efficient and Robust Fitting of Lognormal Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 6(4), pages 95-109.
    5. Blostein, Martin & Miljkovic, Tatjana, 2019. "On modeling left-truncated loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 35-46.
    6. 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.
    7. William H. Aeberhard & Eva Cantoni & Stephane Heritier, 2014. "Robust inference in the negative binomial regression model with an application to falls data," Biometrics, The International Biometric Society, vol. 70(4), pages 920-931, December.
    8. Vytaras Brazauskas & Robert Serfling, 2000. "Robust and Efficient Estimation of the Tail Index of a Single-Parameter Pareto Distribution," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(4), pages 12-27.
    9. Brazauskas, Vytaras & Serfling, Robert, 2003. "Favorable Estimators for Fitting Pareto Models: A Study Using Goodness-of-fit Measures with Actual Data," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 365-381, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Brazauskas, Vytaras, 2003. "Influence functions of empirical nonparametric estimators of net reinsurance premiums," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 115-133, February.
    3. Su, Jianxi & Furman, Edward, 2017. "Multiple risk factor dependence structures: Distributional properties," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 56-68.
    4. Milan Stehlík & Rastislav Potocký & Helmut Waldl & Zdeněk Fabián, 2010. "On the favorable estimation for fitting heavy tailed data," Computational Statistics, Springer, vol. 25(3), pages 485-503, September.
    5. 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.
    6. Asimit, Alexandru V. & Badescu, Alexandru M. & Verdonck, Tim, 2013. "Optimal risk transfer under quantile-based risk measurers," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 252-265.
    7. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    8. Aeberhard, William H. & Cantoni, Eva & Heritier, Stephane, 2017. "Saddlepoint tests for accurate and robust inference on overdispersed count data," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 162-175.
    9. Richard S. J. Tol, 2024. "The climate niche of Homo Sapiens," Climatic Change, Springer, vol. 177(6), pages 1-17, June.
    10. Lanyu Xiong & Fukang Zhu, 2024. "Robust estimation for the one-parameter exponential family integer-valued GARCH(1,1) models based on a modified Tukey’s biweight function," Computational Statistics, Springer, vol. 39(2), pages 495-522, April.
    11. Aaron Clauset & Maxwell Young & Kristian Skrede Gleditsch, 2007. "On the Frequency of Severe Terrorist Events," Journal of Conflict Resolution, Peace Science Society (International), vol. 51(1), pages 58-87, February.
    12. Zhou, Weihua & Serfling, Robert, 2008. "Generalized multivariate rank type test statistics via spatial U-quantiles," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 376-383, March.
    13. James Allison & Bojana Milošević & Marko Obradović & Marius Smuts, 2022. "Distribution-free goodness-of-fit tests for the Pareto distribution based on a characterization," Computational Statistics, Springer, vol. 37(1), pages 403-418, March.
    14. N. Balakrishnan & Helton Saulo & Marcelo Bourguignon & Xiaojun Zhu, 2017. "On moment-type estimators for a class of log-symmetric distributions," Computational Statistics, Springer, vol. 32(4), pages 1339-1355, December.
    15. J. D. Opdyke, 2014. "Estimating Operational Risk Capital with Greater Accuracy, Precision, and Robustness," Papers 1406.0389, arXiv.org, revised Nov 2014.
    16. Alfio Marazzi & Marina Valdora & Victor Yohai & Michael Amiguet, 2019. "A robust conditional maximum likelihood estimator for generalized linear models with a dispersion parameter," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 223-241, March.
    17. 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.
    18. Ayanendranath Basu & Abhik Ghosh & Abhijit Mandal & Nirian Martin & Leandro Pardo, 2021. "Robust Wald-type tests in GLM with random design based on minimum density power divergence estimators," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 973-1005, September.
    19. Hubert, Mia & Dierckx, Goedele & Vanpaemel, Dina, 2013. "Detecting influential data points for the Hill estimator in Pareto-type distributions," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 13-28.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metrik:v:88:y:2025:i:2:d:10.1007_s00184-024-00952-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.