IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v66y2025i6d10.1007_s00362-025-01755-1.html
   My bibliography  Save this article

One-step statistical estimation method for generalized linear models

Author

Listed:
  • Alexandre Brouste

    (Le Mans Université)

  • Lilit Hovsepyan

    (Le Mans Université)

  • Irene Votsi

    (Université de Lorraine)

Abstract

In this article, the one-step estimation procedure is presented for generalized linear models. In these models, the maximum likelihood estimator, which is asymptotically efficient, has no closed-form and gradient-descent methods are generally used for its numerical computation. Nevertheless, when the amount of data is large and/or the number of explanatory variables is high, then the computations can be very consuming. To overcome this difficulty, the one-step estimation procedure is used, which is based on an initial (inefficient) guess estimator and a single step of the Fisher scoring. The main advantage of this procedure is that only one iterative step is required to achieve the asymptotic efficiency. The results are validated numerically by means of Monte-Carlo simulations.The estimation procedure is used to fit generalized linear models for climate risk insurance data.

Suggested Citation

  • Alexandre Brouste & Lilit Hovsepyan & Irene Votsi, 2025. "One-step statistical estimation method for generalized linear models," Statistical Papers, Springer, vol. 66(6), pages 1-19, October.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:6:d:10.1007_s00362-025-01755-1
    DOI: 10.1007/s00362-025-01755-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-025-01755-1
    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/s00362-025-01755-1?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Kengo Kamatani & Masayuki Uchida, 2015. "Hybrid multi-step estimators for stochastic differential equations based on sampled data," Statistical Inference for Stochastic Processes, Springer, vol. 18(2), pages 177-204, July.
    2. Papastamoulis, Panagiotis & Martin-Magniette, Marie-Laure & Maugis-Rabusseau, Cathy, 2016. "On the estimation of mixtures of Poisson regression models with large number of components," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 97-106.
    3. Ghosal, Rahul & Ghosh, Sujit K., 2022. "Bayesian inference for generalized linear model with linear inequality constraints," Computational Statistics & Data Analysis, Elsevier, vol. 166(C).
    4. Christophe Dutang, 2017. "Some explanations about the IWLS algorithm to fit generalized linear models," Working Papers hal-01577698, HAL.
    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. Fourrier-Nicolaï Edwin & Lubrano Michel, 2024. "Bayesian inference for non-anonymous growth incidence curves using Bernstein polynomials: an application to academic wage dynamics," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 28(2), pages 319-336, April.
    2. Papastamoulis, Panagiotis, 2018. "Overfitting Bayesian mixtures of factor analyzers with an unknown number of components," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 220-234.
    3. Lluís Bermúdez & Dimitris Karlis & Isabel Morillo, 2020. "Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models," Risks, MDPI, vol. 8(1), pages 1-13, January.
    4. Yozo Tonaki & Yusuke Kaino & Masayuki Uchida, 2022. "Adaptive tests for parameter changes in ergodic diffusion processes from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 397-430, July.
    5. Masahiro Kurisaki, 2023. "Parameter estimation for ergodic linear SDEs from partial and discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 279-330, July.
    6. Shoichi Eguchi & Hiroki Masuda, 2019. "Data driven time scale in Gaussian quasi-likelihood inference," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 383-430, October.
    7. Alessandro Gregorio & Francesco Iafrate, 2021. "Regularized bridge-type estimation with multiple penalties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 921-951, October.
    8. Anne-Sophie Krah & Zoran Nikolić & Ralf Korn, 2020. "Machine Learning in Least-Squares Monte Carlo Proxy Modeling of Life Insurance Companies," Risks, MDPI, vol. 8(1), pages 1-79, February.
    9. Kutoyants, Yu.A., 2017. "On the multi-step MLE-process for ergodic diffusion," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2243-2261.
    10. Yusuke Kaino & Masayuki Uchida, 2018. "Hybrid estimators for stochastic differential equations from reduced data," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 435-454, July.
    11. Che, Yuyuan & Ghosh, Sujit K. & Rejesus, Roderick M., 2022. "Estimating Production Risk Effects with Inequality Constraints," 2024 Annual Meeting, July 28-30, New Orleans, LA 322189, Agricultural and Applied Economics Association.
    12. Mithun S. Ullal & Iqbal Thonse Hawaldar & Rashmi Soni & Mohammed Nadeem, 2021. "The Role of Machine Learning in Digital Marketing," SAGE Open, , vol. 11(4), pages 21582440211, October.
    13. Shogo H. Nakakita & Yusuke Kaino & Masayuki Uchida, 2021. "Quasi-likelihood analysis and Bayes-type estimators of an ergodic diffusion plus noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 177-225, February.
    14. Lluís Bermúdez & Dimitris Karlis, 2022. "Copula-based bivariate finite mixture regression models with an application for insurance claim count data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1082-1099, December.
    15. Simon Clinet, 2020. "Quasi-likelihood analysis for marked point processes and application to marked Hawkes processes," Papers 2001.11624, arXiv.org, revised Aug 2021.
    16. Yusuke Kaino & Masayuki Uchida, 2018. "Hybrid estimators for small diffusion processes based on reduced data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 745-773, October.
    17. Anne-Sophie Krah & Zoran Nikoli'c & Ralf Korn, 2019. "Machine Learning in Least-Squares Monte Carlo Proxy Modeling of Life Insurance Companies," Papers 1909.02182, arXiv.org.
    18. A. Gregorio & S. M. Iacus, 2019. "Empirical $$L^2$$ L 2 -distance test statistics for ergodic diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 233-261, July.
    19. Yu. A. Kutoyants & A. Motrunich, 2016. "On multi-step MLE-process for Markov sequences," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(6), pages 705-724, August.
    20. Tonaki, Yozo & Uchida, Masayuki, 2023. "Change point inference in ergodic diffusion processes based on high frequency data," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 1-39.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:stpapr:v:66:y:2025:i:6:d:10.1007_s00362-025-01755-1. 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.