IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v62y2021i2d10.1007_s00362-019-01123-w.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-019-01123-w
    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/s00362-019-01123-w?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. 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.
    2. Kiefer, Nicholas M & Skoog, Gary R, 1984. "Local Asymptotic Specification Error Analysis," Econometrica, Econometric Society, vol. 52(4), pages 873-885, July.
    3. A. Saleh & B. Kibria, 2013. "Improved ridge regression estimators for the logistic regression model," Computational Statistics, Springer, vol. 28(6), pages 2519-2558, December.
    4. 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.
    5. 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.
    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. Guoping Zeng & Sha Tao, 2023. "A Generalized Linear Transformation and Its Effects on Logistic Regression," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    2. M Arashi & M Roozbeh & N A Hamzah & M Gasparini, 2021. "Ridge regression and its applications in genetic studies," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-17, April.
    3. M. Arashi & Mahdi Roozbeh, 2019. "Some improved estimation strategies in high-dimensional semiparametric regression models with application to riboflavin production data," Statistical Papers, Springer, vol. 60(3), pages 667-686, June.
    4. Esmeralda Ramalho, 2004. "Covariate Measurement Error in Endogenous Stratified Samples," Economics Working Papers 2_2004, University of Évora, Department of Economics (Portugal).
    5. Mohammad Arashi & Mina Norouzirad & Mahdi Roozbeh & Naushad Mamode Khan, 2021. "A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations," Mathematics, MDPI, vol. 9(23), pages 1-11, November.
    6. Francisco J. Gil & Maria Jesus Martin & Angel Serrat, 1994. "Movilidad en el mercado de trabajo en España: un análisis econométrico de duración con riesgos en competencia," Investigaciones Economicas, Fundación SEPI, vol. 18(3), pages 517-537, September.
    7. Carlsson, Fredrik & Johansson-Stenman, Olof, 2006. "Should We Trust Hypothetical Referenda? Test and Identification Problems," Working Papers in Economics 189, University of Gothenburg, Department of Economics, revised 24 Jan 2006.
    8. James R. Brown, 2005. "Venture Capital and Firm Performance Over the Long-Run: Evidence from High-Tech IPOs in the United States," Journal of Entrepreneurial Finance, Pepperdine University, Graziadio School of Business and Management, vol. 10(3), pages 1-33, Fall.
    9. Klein, T.J., 2010. "Heterogeneous treatment effects : Instrumental variables without monotonicity?," Other publications TiSEM 0ec85b01-ab6a-4c2a-9e23-1, Tilburg University, School of Economics and Management.
    10. Hadi Emami, 2018. "Local influence for Liu estimators in semiparametric linear models," Statistical Papers, Springer, vol. 59(2), pages 529-544, June.
    11. 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.
    12. Klein, Tobias J., 2010. "Heterogeneous treatment effects: Instrumental variables without monotonicity?," Journal of Econometrics, Elsevier, vol. 155(2), pages 99-116, April.
    13. Murphy, Anthony, 1996. "Simple LM tests of mis-specification for ordered logit models," Economics Letters, Elsevier, vol. 52(2), pages 137-141, August.
    14. Saleh, A.K.Md. Ehsanes & Shalabh,, 2014. "A ridge regression estimation approach to the measurement error model," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 68-84.
    15. Roozbeh, Mahdi, 2016. "Robust ridge estimator in restricted semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 127-144.
    16. Carlsson, Fredrik & Johansson-Stenman, Olof, 2010. "Scale factors and hypothetical referenda: A clarifying note," Journal of Environmental Economics and Management, Elsevier, vol. 59(3), pages 286-292, May.
    17. Franco Peracchi, 1988. "Robust M-Estimators," UCLA Economics Working Papers 477, UCLA Department of Economics.
    18. West, Kenneth D., 1986. "Full-versus limited-information estimation of a rational-expectations model: Some numerical comparisons," Journal of Econometrics, Elsevier, vol. 33(3), pages 367-385, December.
    19. M. Arashi & T. Valizadeh, 2015. "Performance of Kibria’s methods in partial linear ridge regression model," Statistical Papers, Springer, vol. 56(1), pages 231-246, February.
    20. Ahmed, S. Ejaz & Nicol, Christopher J., 2012. "An application of shrinkage estimation to the nonlinear regression model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3309-3321.

    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:62:y:2021:i:2:d:10.1007_s00362-019-01123-w. 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.