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Rank-based Liu regression

Author

Listed:
  • Mohammad Arashi

    (Shahrood University of Technology)

  • Mina Norouzirad

    (Shahrood University of Technology)

  • S. Ejaz Ahmed

    (University of Brock)

  • Bahadır Yüzbaşı

    (University of Inonu)

Abstract

Due to the complicated mathematical and nonlinear nature of ridge regression estimator, Liu (Linear-Unified) estimator has been received much attention as a useful method to overcome the weakness of the least square estimator, in the presence of multicollinearity. In situations where in the linear model, errors are far away from normal or the data contain some outliers, the construction of Liu estimator can be revisited using a rank-based score test, in the line of robust regression. In this paper, we define the Liu-type rank-based and restricted Liu-type rank-based estimators when a sub-space restriction on the parameter of interest holds. Accordingly, some improved estimators are defined and their asymptotic distributional properties are investigated. The conditions of superiority of the proposed estimators for the biasing parameter are given. Some numerical computations support the findings of the paper.

Suggested Citation

  • Mohammad Arashi & Mina Norouzirad & S. Ejaz Ahmed & Bahadır Yüzbaşı, 2018. "Rank-based Liu regression," Computational Statistics, Springer, vol. 33(3), pages 1525-1561, September.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:3:d:10.1007_s00180-018-0809-8
    DOI: 10.1007/s00180-018-0809-8
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    References listed on IDEAS

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    3. 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.
    4. Esra Akdeniz Duran & Fikri Akdeniz, 2012. "Efficiency of the modified jackknifed Liu-type estimator," Statistical Papers, Springer, vol. 53(2), pages 265-280, May.
    5. 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.
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    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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    9. Arashi, M. & Kibria, B.M. Golam & Norouzirad, M. & Nadarajah, S., 2014. "Improved preliminary test and Stein-rule Liu estimators for the ill-conditioned elliptical linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 53-74.
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