IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v194y2024ics0167947324000045.html
   My bibliography  Save this article

Robust heavy-tailed versions of generalized linear models with applications in actuarial science

Author

Listed:
  • Gagnon, Philippe
  • Wang, Yuxi

Abstract

Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are not robust against outliers (i.e., against erroneous or extreme data points). A difference in trends in the bulk of the data and the outliers thus yields skewed inference and predictions. To address this problem, robust methods have been introduced. The most commonly applied robust method is frequentist and consists in an estimator which is derived from a modification of the derivative of the log-likelihood. The objective is to propose an alternative approach which is modelling-based and thus fundamentally different. Such an approach allows for an understanding and interpretation of the modelling, and it can be applied for both frequentist and Bayesian statistical analyses. The proposed approach possesses appealing theoretical and empirical properties.

Suggested Citation

  • Gagnon, Philippe & Wang, Yuxi, 2024. "Robust heavy-tailed versions of generalized linear models with applications in actuarial science," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:csdana:v:194:y:2024:i:c:s0167947324000045
    DOI: 10.1016/j.csda.2024.107920
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947324000045
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2024.107920?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. P. G. Bissiri & C. C. Holmes & S. G. Walker, 2016. "A general framework for updating belief distributions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(5), pages 1103-1130, November.
    2. Alain Desgagné & Jean-François Angers, 2007. "Conflicting information and location parameter inference," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 67-97.
    3. Ken J. Beath, 2018. "A mixture-based approach to robust analysis of generalised linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(12), pages 2256-2268, September.
    4. Jose Ailton Alencar Andrade & Anthony O'Hagan, 2011. "Bayesian Robustness Modelling of Location and Scale Parameters," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(4), pages 691-711, December.
    5. Hamura, Yasuyuki & Irie, Kaoru & Sugasawa, Shonosuke, 2022. "Log-regularly varying scale mixture of normals for robust regression," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    6. Philippe Gagnon & Mylène Bédard & Alain Desgagné, 2021. "An automatic robust Bayesian approach to principal component regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(1), pages 84-104, January.
    7. George R. Terrell, 2003. "The Wilson--Hilferty transformation is locally saddlepoint," Biometrika, Biometrika Trust, vol. 90(2), pages 445-453, June.
    8. Cantoni, Eva & Ronchetti, Elvezio, 2006. "A robust approach for skewed and heavy-tailed outcomes in the analysis of health care expenditures," Journal of Health Economics, Elsevier, vol. 25(2), pages 198-213, March.
    9. Cantoni E. & Ronchetti E., 2001. "Robust Inference for Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1022-1030, September.
    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. 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.
    2. Gagnon, Philippe & Hayashi, Yoshiko, 2023. "Theoretical properties of Bayesian Student-t linear regression," Statistics & Probability Letters, Elsevier, vol. 193(C).
    3. Miron, Julien & Poilane, Benjamin & Cantoni, Eva, 2022. "Robust polytomous logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    4. Graciela Boente & Daniela Rodriguez & Pablo Vena, 2020. "Robust estimators in a generalized partly linear regression model under monotony constraints," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 50-89, March.
    5. Bianco, Ana M. & Boente, Graciela & Rodrigues, Isabel M., 2013. "Robust tests in generalized linear models with missing responses," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 80-97.
    6. Bianco, Ana M. & Boente, Graciela & Rodrigues, Isabel M., 2013. "Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 209-226.
    7. Borislava Mihaylova & Andrew Briggs & Anthony O'Hagan & Simon G. Thompson, 2011. "Review of statistical methods for analysing healthcare resources and costs," Health Economics, John Wiley & Sons, Ltd., vol. 20(8), pages 897-916, August.
    8. Bianco, Ana M. & Martínez, Elena, 2009. "Robust testing in the logistic regression model," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4095-4105, October.
    9. Courbage, Christophe & Rey, Béatrice, 2012. "Priority setting in health care and higher order degree change in risk," Journal of Health Economics, Elsevier, vol. 31(3), pages 484-489.
    10. Crucinio, Francesca R. & De Bortoli, Valentin & Doucet, Arnaud & Johansen, Adam M., 2024. "Solving a class of Fredholm integral equations of the first kind via Wasserstein gradient flows," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    11. Malmendier, Ulrike & Pouzo, Demian & Vanasco, Victoria, 2020. "Investor experiences and international capital flows," Journal of International Economics, Elsevier, vol. 124(C).
    12. Romain Fournier & Zoi Tsangalidou & David Reich & Pier Francesco Palamara, 2023. "Haplotype-based inference of recent effective population size in modern and ancient DNA samples," Nature Communications, Nature, vol. 14(1), pages 1-13, December.
    13. Toru Kitagawa & Hugo Lopez & Jeff Rowley, 2022. "Stochastic Treatment Choice with Empirical Welfare Updating," Papers 2211.01537, arXiv.org, revised Feb 2023.
    14. Jens Klooster & Mikhail Zhelonkin, 2024. "Outlier robust inference in the instrumental variable model with applications to causal effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 86-106, January.
    15. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    16. Ruben Loaiza‐Maya & Gael M. Martin & David T. Frazier, 2021. "Focused Bayesian prediction," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(5), pages 517-543, August.
    17. Fiaschi, Davide & Giuliani, Elisa & Nieri, Federica & Salvati, Nicola, 2020. "How bad is your company? Measuring corporate wrongdoing beyond the magic of ESG metrics," Business Horizons, Elsevier, vol. 63(3), pages 287-299.
    18. Ricardo A. Maronna & Victor J. Yohai, 2021. "Optimal robust estimators for families of distributions on the integers," Statistical Papers, Springer, vol. 62(5), pages 2269-2281, October.
    19. James Dawber & Nicola Salvati & Enrico Fabrizi & Nikos Tzavidis, 2022. "Expectile regression for multi‐category outcomes with application to small area estimation of labour force participation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 590-619, December.
    20. Krichene, H. & Geiger, T. & Frieler, K. & Willner, S.N. & Sauer, I. & Otto, C., 2021. "Long-term impacts of tropical cyclones and fluvial floods on economic growth – Empirical evidence on transmission channels at different levels of development," World Development, Elsevier, vol. 144(C).

    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:eee:csdana:v:194:y:2024:i:c:s0167947324000045. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.