Computational Statistics

, Volume 33, Issue 3, pp 1525–1561 | Cite as

Rank-based Liu regression

  • Mohammad Arashi
  • Mina Norouzirad
  • S. Ejaz Ahmed
  • Bahadır Yüzbaşı
Original Paper


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.


Liu estimator Multicollinearity Preliminary test Rank-based estimator Ridge regression Shrinkage estimator 



We would like to thank two anonymous referees for their valuable and constructive comments which significantly improved the presentation of the paper and led to put many details. First author Mohammad Arashi’s work is based on the research supported in part by the National Research Foundation of South Africa (Grant NO. 109214). Third author S. Ejaz Ahmed is supported by the Natural Sciences and the Engineering Research Council of Canada (NSERC).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Statistics, Faculty of Mathematical SciencesShahrood University of TechnologyShahroodIran
  2. 2.Department of Mathematics and StatisticsUniversity of BrockSt. CatharinesCanada
  3. 3.Department of EconometricsUniversity of InonuMalatyaTurkey

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