Combating Multicollinearity: A New Two-Parameter Approach

Abstract

The ordinary least square (OLS) estimator is the Best Linear Unbiased Estimator (BLUE) when all linear regression model assumptions are valid. The OLS estimator, however, becomes inefficient in the presence of multicollinearity. Various one and two-parameter estimators have been proposed to circumvent the problem of multicollinearity. This paper presents a new twoparameter estimator called Liu-Kibria Lukman Estimator (LKL) estimator. The proposed estimator is compared theoretically and through Monte Carlo simulation with existing estimators such as the ordinary least square, ordinary ridge regression, Liu, Kibria-Lukman, and Modified Ridge estimators. The results show that the proposed estimator performs better than existing estimators considered in this study under some conditions, using the mean square error criterion. A real-life application to Portland cement and Longley datasets supported the theoretical and simulation results by giving the smallest mean square error compared to the existing estimators.