Statistical Papers

, 47:471 | Cite as

Improvement of the Liu estimator in linear regression model

  • M. H. Hubert
  • P. Wijekoon


In the presence of stochastic prior information, in addition to the sample, Theil and Goldberger (1961) introduced a Mixed Estimator \(\hat \beta _m \) for the parameter vector β in the standard multiple linear regression model (T,2 I). Recently, the Liu estimator which is an alternative biased estimator for β has been proposed by Liu (1993).

In this paper we introduce another new Liu type biased estimator called Stochastic restricted Liu estimator \(\hat \beta _{srd} \) for β, and discuss its efficiency. The necessary and sufficient conditions for mean squared error matrix of the Stochastic restricted Liu estimator \(\hat \beta _{srd} \) to exceed the mean squared error matrix of the mixed estimator \(\hat \beta _m \) will be derived for the two cases in which the parametric restrictions are correct and are not correct. In particular we show that this new biased estimator is superior in the mean squared error matrix sense to both the Mixed estimator \(\hat \beta _m \) and to the biased estimator introduced by Liu (1993).

Key Words

Ordinary least squares estimator, mixed estimator Liu estimator Stochastic Restricted Liu estimator Mean Squared error matrix 


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • M. H. Hubert
    • 1
  • P. Wijekoon
    • 2
  1. 1.Department of Economics and Management, Vavuniya CampusUniversity of JaffnaSri Lanka
  2. 2.Department of Statistics and Computer Science, Faculty of ScienceUniversity of PeradeniyaPeradeniyaSri Lanka

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