An Almost Unbiased Regression Estimator: Theoretical Comparison and Numerical Comparison in Portland Cement Data

Abstract

Multicollinearity is the problem when there is linear dependency among the independent variables. The Ordinary least squares estimator (OLSE) that is commonly adopted is not suitable for the linear regression model when the independent variables are correlated. This is due to the high variance in OLSE and hence the accuracy of OLSE reduces in the presence of multicollinearity. Hence, the estimator named k-almost unbiased regression estimator (KAURE) was proposed as an alternative to OLSE in this paper. KAURE was developed by using the definition of an almost unbiased estimator to further reduce the bias of Liu-type estimator-special case (LTESC). The properties of KAURE including bias, variance-covariance and mean squared error (MSE) were derived. Theoretical comparison and real-life data comparison were carried out to evaluate the performance of the KAURE based on the MSE criterion. The application of the real-life data supported the theoretical comparison that showed the superiority of KAURE over OLSE and LTESC. The results revealed that KAURE could be considered as an alternative estimator for the linear regression model to combat the problem of multicollinearity.