The Traditional Ordinary Least Squares Estimator under Collinearity

In a multiple regression analysis, it is usually difficult to interpret the estimator of the individual coefficients if the explanatory variables are highly inter-correlated. Such aproblem is often referred to as the multicollinearity problem. There exist several ways to solve this problem. One such way is ridge regression. Two approaches of estimating the shrinkage ridge parameter k are proposed. 

Comparison is made with other ridge-type estimators. To investigate the performance of our proposed methods with the traditional ordinary least squares (OLS) and the other approaches for estimating the parameters of the ridge regression model, we calculate the mean squares error (MSE) using thesimulation techniques. Results of the simulation study shows that the suggested ridge regression outperforms both the OLS estimator and the other ridge-type estimators in all of the different situations evaluated in this paper.