On the Restricted Liu Estimator in the Gauss–Markov Model

Abstract

In this paper, we compare two estimators, the RLE (restricted Liu estimator) and the RLSE (restricted least squares estimator) of parameters in linear models under Gauss–Markov models. Using generalized inverse of matrices, we found some equivalency conditions for the superiority of the RLE with respect to the MSE criterion.

Keywords:

• Gauss–Markov model
• Least squares estimator
• Liu estimator
• Multicollinearity
• Restricted least squares estimator
• Restricted Liu estimator

AMS Classification:

• Primary 62J05
• Secondary 62H12

Acknowledgment

The authors wish to thank the referee for a careful reading of the manuscript and for helpful comments.