A NEW RESTRICTED ESTIMATOR IN MULTIPLE LINEAR REGRESSION MODEL

M. I. Alheety (India) and S. D. Gore (India)

Received June 10, 2007; Revised July 25, 2007

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.