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Improved ridge regression estimators for the logistic regression model

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  • 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
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    References listed on IDEAS

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    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.
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    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.
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    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.

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