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Shrinkage Estimation Strategies in Generalised Ridge Regression Models: Low/High‐Dimension Regime

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  • Bahadır Yüzbaşı
  • Mohammad Arashi
  • S. Ejaz Ahmed

Abstract

In this study, we suggest pretest and shrinkage methods based on the generalised ridge regression estimation that is suitable for both multicollinear and high‐dimensional problems. We review and develop theoretical results for some of the shrinkage estimators. The relative performance of the shrinkage estimators to some penalty methods is compared and assessed by both simulation and real‐data analysis. We show that the suggested methods can be accounted as good competitors to regularisation techniques, by means of a mean squared error of estimation and prediction error. A thorough comparison of pretest and shrinkage estimators based on the maximum likelihood method to the penalty methods. In this paper, we extend the comparison outlined in his work using the least squares method for the generalised ridge regression.

Suggested Citation

  • Bahadır Yüzbaşı & Mohammad Arashi & S. Ejaz Ahmed, 2020. "Shrinkage Estimation Strategies in Generalised Ridge Regression Models: Low/High‐Dimension Regime," International Statistical Review, International Statistical Institute, vol. 88(1), pages 229-251, April.
    • Handle: RePEc:bla:istatr:v:88:y:2020:i:1:p:229-251
    DOI: 10.1111/insr.12351
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Roozbeh, Mahdi, 2015. "Shrinkage ridge estimators in semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 56-74.
    3. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    4. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    5. Mahdi Roozbeh & Mohammad Arashi, 2016. "Shrinkage ridge regression in partial linear models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(20), pages 6022-6044, October.
    6. Xiaoli Gao & S. E. Ahmed & Yang Feng, 2017. "Post selection shrinkage estimation for high‐dimensional data analysis," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(2), pages 97-120, March.
    7. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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    Cited by:

    1. Bahadır Yüzbaşı & S. Ejaz Ahmed, 2020. "Ridge Type Shrinkage Estimation of Seemingly Unrelated Regressions And Analytics of Economic and Financial Data from “Fragile Five” Countries," JRFM, MDPI, vol. 13(6), pages 1-19, June.

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