IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v35y2020i2d10.1007_s00180-019-00918-7.html
   My bibliography  Save this article

Closed-form maximum likelihood estimator for generalized linear models in the case of categorical explanatory variables: application to insurance loss modeling

Author

Listed:
  • Alexandre Brouste

    (Le Mans Université)

  • Christophe Dutang

    (Univ. Paris-Dauphine, Univ. PSL)

  • Tom Rohmer

    (Le Mans Université)

Abstract

Generalized linear models with categorical explanatory variables are considered and parameters of the model are estimated by an exact maximum likelihood method. The existence of a sequence of maximum likelihood estimators is discussed and considerations on possible link functions are proposed. A focus is then given on two particular positive distributions: the Pareto 1 distribution and the shifted log-normal distributions. Finally, the approach is illustrated on an actuarial dataset to model insurance losses.

Suggested Citation

  • Alexandre Brouste & Christophe Dutang & Tom Rohmer, 2020. "Closed-form maximum likelihood estimator for generalized linear models in the case of categorical explanatory variables: application to insurance loss modeling," Computational Statistics, Springer, vol. 35(2), pages 689-724, June.
  • Handle: RePEc:spr:compst:v:35:y:2020:i:2:d:10.1007_s00180-019-00918-7
    DOI: 10.1007/s00180-019-00918-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-019-00918-7
    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/s00180-019-00918-7?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. Stan Lipovetsky, 2015. "Analytical closed-form solution for binary logit regression by categorical predictors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(1), pages 37-49, January.
    2. Beirlant, Jan & Goegebeur, Yuri, 2003. "Regression with response distributions of Pareto-type," Computational Statistics & Data Analysis, Elsevier, vol. 42(4), pages 595-619, April.
    3. Beirlant, Jan & Goegebeur, Yuri & Verlaak, Robert & Vynckier, Petra, 1998. "Burr regression and portfolio segmentation," Insurance: Mathematics and Economics, Elsevier, vol. 23(3), pages 231-250, December.
    4. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    5. Ozkok, Erengul & Streftaris, George & Waters, Howard R. & Wilkie, A. David, 2012. "Bayesian modelling of the time delay between diagnosis and settlement for Critical Illness Insurance using a Burr generalised-linear-type model," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 266-279.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christophe Dutang & Quentin Guibert, 2021. "An explicit split point procedure in model-based trees allowing for a quick fitting of GLM trees and GLM forests," Post-Print hal-03448250, HAL.
    2. Alexandre Brouste & Christophe Dutang & Tom Rohmer, 2022. "A Closed-form Alternative Estimator for GLM with Categorical Explanatory Variables," Post-Print hal-03689206, HAL.

    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. Julien Hambuckers & Marie Kratz & Antoine Usseglio-Carleve, 2023. "Efficient Estimation In Extreme Value Regression Models Of Hedge Fund Tail Risks," Working Papers hal-04090916, HAL.
    2. Bhati, Deepesh & Ravi, Sreenivasan, 2018. "On generalized log-Moyal distribution: A new heavy tailed size distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 247-259.
    3. Julien Hambuckers & Marie Kratz & Antoine Usseglio-Carleve, 2023. "Efficient Estimation in Extreme Value Regression Models of Hedge Fund Tail Risks," Papers 2304.06950, arXiv.org.
    4. Ozkok, Erengul & Streftaris, George & Waters, Howard R. & Wilkie, A. David, 2012. "Bayesian modelling of the time delay between diagnosis and settlement for Critical Illness Insurance using a Burr generalised-linear-type model," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 266-279.
    5. Abduraimova, Kumushoy, 2022. "Contagion and tail risk in complex financial networks," Journal of Banking & Finance, Elsevier, vol. 143(C).
    6. Yixuan Wang & Jianzhu Li & Ping Feng & Rong Hu, 2015. "A Time-Dependent Drought Index for Non-Stationary Precipitation Series," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(15), pages 5631-5647, December.
    7. Nathaniel Geiger & Bryan McLaughlin & John Velez, 2021. "Not all boomers: temporal orientation explains inter- and intra-cultural variability in the link between age and climate engagement," Climatic Change, Springer, vol. 166(1), pages 1-20, May.
    8. Panayi, Efstathios & Peters, Gareth W. & Danielsson, Jon & Zigrand, Jean-Pierre, 2018. "Designating market maker behaviour in limit order book markets," Econometrics and Statistics, Elsevier, vol. 5(C), pages 20-44.
    9. Gauss Cordeiro & Josemar Rodrigues & Mário Castro, 2012. "The exponential COM-Poisson distribution," Statistical Papers, Springer, vol. 53(3), pages 653-664, August.
    10. Christian Kleiber & Achim Zeileis, 2016. "Visualizing Count Data Regressions Using Rootograms," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 296-303, July.
    11. Chen, Shu & Shao, Dongguo & Tan, Xuezhi & Gu, Wenquan & Lei, Caixiu, 2017. "An interval multistage classified model for regional inter- and intra-seasonal water management under uncertain and nonstationary condition," Agricultural Water Management, Elsevier, vol. 191(C), pages 98-112.
    12. Riccardo De Bin & Vegard Grødem Stikbakke, 2023. "A boosting first-hitting-time model for survival analysis in high-dimensional settings," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 420-440, April.
    13. Matteo Malavasi & Gareth W. Peters & Pavel V. Shevchenko & Stefan Truck & Jiwook Jang & Georgy Sofronov, 2021. "Cyber Risk Frequency, Severity and Insurance Viability," Papers 2111.03366, arXiv.org, revised Mar 2022.
    14. Joanna Baj-Korpak & Marian Jan Stelmach & Kamil Zaworski & Piotr Lichograj & Marek Wochna, 2022. "Assessment of Motor Abilities and Physical Fitness in Youth in the Context of Talent Identification—OSF Test," IJERPH, MDPI, vol. 19(21), pages 1-19, November.
    15. Youxin Wang & Tao Peng & Qingxia Lin & Vijay P. Singh & Xiaohua Dong & Chen Chen & Ji Liu & Wenjuan Chang & Gaoxu Wang, 2022. "A New Non-stationary Hydrological Drought Index Encompassing Climate Indices and Modified Reservoir Index as Covariates," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(7), pages 2433-2454, May.
    16. Lucio Masserini & Matilde Bini & Monica Pratesi, 2017. "Effectiveness of non-selective evaluation test scores for predicting first-year performance in university career: a zero-inflated beta regression approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 693-708, March.
    17. Hötte, Kerstin, 2023. "Demand-pull, technology-push, and the direction of technological change," Research Policy, Elsevier, vol. 52(5).
    18. Lipovetsky, Stan, 2018. "Quantum paradigm of probability amplitude and complex utility in entangled discrete choice modeling," Journal of choice modelling, Elsevier, vol. 27(C), pages 62-73.
    19. Simon N. Wood & Natalya Pya & Benjamin Säfken, 2016. "Smoothing Parameter and Model Selection for General Smooth Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1548-1563, October.
    20. Dominique Guegan & Bertrand K. Hassani, 2011. "Operational risk: a Basel II++ step before Basel III," Documents de travail du Centre d'Economie de la Sorbonne 11053, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

    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:compst:v:35:y:2020:i:2:d:10.1007_s00180-019-00918-7. 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.