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Ridge-type shrinkage estimators in generalized linear models with an application to prostate cancer data

Author

Listed:
  • M. Nooi Asl

    (University of Tabriz)

  • H. Bevrani

    (University of Tabriz)

  • R. Arabi Belaghi

    (University of Tabriz)

  • K. Mansson

    (Jonkoping University)

Abstract

This paper is concerned with the estimation of the regression coefficients for the generalized linear models in the situation where a multicollinear issue exists and when it is suspected that some of the regression coefficients may be restricted to a linear subspace. Accordingly, as a solution to this issue, we propose a new Stein-type shrinkage ridge estimation approach. We provide the analytic expressions for the asymptotic biases and risks of the proposed estimators and investigate their relative performance with respect to the unrestricted ridge regression estimator. Monte-Carlo simulation studies are conducted to appraise the performance of the underlying estimators in terms of their simulated relative efficiencies. It is clear from both the analytical results and the simulation study that the Stein-type shrinkage ridge estimators dominate the usual ridge regression estimator in the entire parameter space. Finally an empirical application is provided where prostate cancer data is analyzed to show the practical usefulness of the suggested approach. Based on the results from the different parts of this paper, we find that the new method developed would be useful for the practitioners in various research areas such as economics, insurance data and medicine.

Suggested Citation

  • M. Nooi Asl & H. Bevrani & R. Arabi Belaghi & K. Mansson, 2021. "Ridge-type shrinkage estimators in generalized linear models with an application to prostate cancer data," Statistical Papers, Springer, vol. 62(2), pages 1043-1085, April.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:2:d:10.1007_s00362-019-01123-w
    DOI: 10.1007/s00362-019-01123-w
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    References listed on IDEAS

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    1. Kiefer, Nicholas M & Skoog, Gary R, 1984. "Local Asymptotic Specification Error Analysis," Econometrica, Econometric Society, vol. 52(4), pages 873-885, July.
    2. A. Saleh & B. Kibria, 2013. "Improved ridge regression estimators for the logistic regression model," Computational Statistics, Springer, vol. 28(6), pages 2519-2558, December.
    3. Amini, Morteza & Roozbeh, Mahdi, 2015. "Optimal partial ridge estimation in restricted semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 26-40.
    4. Roozbeh, Mahdi, 2018. "Optimal QR-based estimation in partially linear regression models with correlated errors using GCV criterion," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 45-61.
    5. A. Saleh & B. Golam Kibria, 2011. "On some ridge regression estimators: a nonparametric approach," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 819-851.
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    Cited by:

    1. Muhammad Qasim, 2024. "A weighted average limited information maximum likelihood estimator," Statistical Papers, Springer, vol. 65(5), pages 2641-2666, July.

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