IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v28y2013i6p2519-2558.html
   My bibliography  Save this article

Improved ridge regression estimators for the logistic regression model

Author

Listed:
  • A. Saleh
  • B. Kibria

Abstract

The estimation of the regression parameters for the ill-conditioned logistic regression model is considered in this paper. We proposed five ridge regression (RR) estimators, namely, unrestricted RR, restricted ridge regression, preliminary test RR, shrinkage ridge regression and positive rule RR estimators for estimating the parameters $$(\beta )$$ when it is suspected that the parameter $$\beta $$ may belong to a linear subspace defined by $$H\beta =h$$ . Asymptotic properties of the estimators are studied with respect to quadratic risks. The performances of the proposed estimators are compared based on the quadratic bias and risk functions under both null and alternative hypotheses, which specify certain restrictions on the regression parameters. The conditions of superiority of the proposed estimators for departure and ridge parameters are given. Some graphical representations and efficiency analysis have been presented which support the findings of the paper. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • A. Saleh & B. Kibria, 2013. "Improved ridge regression estimators for the logistic regression model," Computational Statistics, Springer, vol. 28(6), pages 2519-2558, December.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:6:p:2519-2558
    DOI: 10.1007/s00180-013-0417-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00180-013-0417-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00180-013-0417-6?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. Ohtani, Kazuhiro, 1993. "A Comparison of the Stein-Rule and Positive-Part Stein-Rule Estimators in a Misspecified Linear Regression Model," Econometric Theory, Cambridge University Press, vol. 9(4), pages 668-679, August.
    2. Shalabh, 1998. "Improved Estimation in Measurement Error Models Through Stein Rule Procedure," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 35-48, October.
    3. B. Kibria & Kristofer Månsson & Ghazi Shukur, 2012. "Performance of Some Logistic Ridge Regression Estimators," Computational Economics, Springer;Society for Computational Economics, vol. 40(4), pages 401-414, December.
    4. Arashi, M. & Tabatabaey, S.M.M., 2008. "Stein-type improvement under stochastic constraints: Use of multivariate Student-t model in regression," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2142-2153, October.
    5. Sarjinder Singh & Derrick Shannon Tracy, 1999. "Ridge regression using scrambled responses," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1-2), pages 147-157.
    6. Arashi, M. & Tabatabaey, S.M.M., 2009. "Improved variance estimation under sub-space restriction," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1752-1760, September.
    7. S. le Cessie & J. C. van Houwelingen, 1992. "Ridge Estimators in Logistic Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 191-201, March.
    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. 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.

    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. 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.
    2. Muhammad Amin & Muhammad Qasim & Muhammad Amanullah & Saima Afzal, 2020. "Performance of some ridge estimators for the gamma regression model," Statistical Papers, Springer, vol. 61(3), pages 997-1026, June.
    3. N. H. Jadhav, 2020. "On linearized ridge logistic estimator in the presence of multicollinearity," Computational Statistics, Springer, vol. 35(2), pages 667-687, June.
    4. Christopher J Greenwood & George J Youssef & Primrose Letcher & Jacqui A Macdonald & Lauryn J Hagg & Ann Sanson & Jenn Mcintosh & Delyse M Hutchinson & John W Toumbourou & Matthew Fuller-Tyszkiewicz &, 2020. "A comparison of penalised regression methods for informing the selection of predictive markers," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-14, November.
    5. František Dařena & Jan Přichystal, 2018. "Analysis of the Association between Topics in Online Documents and Stock Price Movements," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 66(6), pages 1431-1439.
    6. Li Shaoyu & Lu Qing & Fu Wenjiang & Romero Roberto & Cui Yuehua, 2009. "A Regularized Regression Approach for Dissecting Genetic Conflicts that Increase Disease Risk in Pregnancy," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-30, October.
    7. Butaru, Florentin & Chen, Qingqing & Clark, Brian & Das, Sanmay & Lo, Andrew W. & Siddique, Akhtar, 2016. "Risk and risk management in the credit card industry," Journal of Banking & Finance, Elsevier, vol. 72(C), pages 218-239.
    8. Matthew Herland & Richard A. Bauder & Taghi M. Khoshgoftaar, 2020. "Approaches for identifying U.S. medicare fraud in provider claims data," Health Care Management Science, Springer, vol. 23(1), pages 2-19, March.
    9. Paolo Cimbali & Marco De Leonardis & Alessio Fiume & Barbara La Ganga & Luciana Meoli & Marco Orlandi, 2023. "A decision-making rule to detect insufficient data quality - an application of statistical learning techniques to the non-performing loans banking data," IFC Bulletins chapters, in: Bank for International Settlements (ed.), Post-pandemic landscape for central bank statistics, volume 58, Bank for International Settlements.
    10. Cheng, C.-L. & Shalabh, & Garg, G., 2014. "Coefficient of determination for multiple measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 137-152.
    11. Wenfa Li & Hongzhe Liu & Peng Yang & Wei Xie, 2016. "Supporting Regularized Logistic Regression Privately and Efficiently," PLOS ONE, Public Library of Science, vol. 11(6), pages 1-19, June.
    12. M. Revan Özkale & Atif Abbasi, 2022. "Iterative restricted OK estimator in generalized linear models and the selection of tuning parameters via MSE and genetic algorithm," Statistical Papers, Springer, vol. 63(6), pages 1979-2040, December.
    13. Kadri Ulas Akay, 2014. "A graphical evaluation of logistic ridge estimator in mixture experiments," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(6), pages 1217-1232, June.
    14. Marco-Antonio Moreno-Ibarra & Yenny Villuendas-Rey & Miltiadis D. Lytras & Cornelio Yáñez-Márquez & Julio-César Salgado-Ramírez, 2021. "Classification of Diseases Using Machine Learning Algorithms: A Comparative Study," Mathematics, MDPI, vol. 9(15), pages 1-21, July.
    15. Lambert-Lacroix, Sophie & Peyre, Julie, 2006. "Local likelihood regression in generalized linear single-index models with applications to microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 2091-2113, December.
    16. Scott D. Bass & Lukasz A. Kurgan, 2010. "Discovery of factors influencing patent value based on machine learning in patents in the field of nanotechnology," Scientometrics, Springer;Akadémiai Kiadó, vol. 82(2), pages 217-241, February.
    17. Heungsun Hwang & Hye Suk & Yoshio Takane & Jang-Han Lee & Jooseop Lim, 2015. "Generalized Functional Extended Redundancy Analysis," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 101-125, March.
    18. Ying Guan & Guang-Hui Fu, 2022. "A Double-Penalized Estimator to Combat Separation and Multicollinearity in Logistic Regression," Mathematics, MDPI, vol. 10(20), pages 1-19, October.
    19. M Berkan Sesen & Ann E Nicholson & Rene Banares-Alcantara & Timor Kadir & Michael Brady, 2013. "Bayesian Networks for Clinical Decision Support in Lung Cancer Care," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-1, December.
    20. Ayanendranath Basu & Abhik Ghosh & Maria Jaenada & Leandro Pardo, 2024. "Robust adaptive LASSO in high-dimensional logistic regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(5), pages 1217-1249, November.

    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:28:y:2013:i:6:p:2519-2558. 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.