Abstract: In
the literature on multicollinearity, it is noted that one of the major
consequences of it on the ordinary least squares estimator is that the estimator
has a large sampling variance, which in effect might inappropriately lead to
exclusion of otherwise significant variables from the model. To circumvent this
problem, several alternative methods have been suggested to improve the
precision of estimators. In this paper, we introduce a new type of the
restricted estimators so-called restricted maximum likelihood Liu estimator by
augmenting to the linear model and then consider a set of linear
restrictions on b. We investigate the properties of this
estimator and find that this estimator has smaller variance than the restricted
least squares estimator and Liu estimator. The standard property of this new
estimator has been studied in this paper. It has also been shown that this
estimator is superior to the Liu and Restricted least squares estimator by the
criterion of mean square error matrix when the restrictions are indeed true.
Keywords and phrases: restricted least squares estimator, multicollinearity, Liu estimator, mean squared error, restricted maximum likelihood Liu estimator.
