Comparison of Restricted and Unrestricted estimators with a Monte-Carlo Simulation Study

This study deals with the problem of multicollinearity in the linear regression model. Restricted and unrestricted parameter estimates are chosen among biased estimators to be studied and compared as two corresponding groups, with the aim of identifying which group gives better parameter estimates in the case of multicollinearity. Estimators' performance is compared according to matrix mean square error and scalar mean square error. Proceeding from this, it has been shown that, in the sense of Scalar Mean Square Error (SMSE), the Restricted Ridge regression (RRR) estimator outperforms all constrained and unconstrained estimators, while the Ridge regression is superior to the unconstrained set of estimators. A real-life application and Monte-Carlo simulation study are conducted to compare the performance of restricted and unrestricted estimators. As a result, it was decided that the most effective estimators are the restricted biased estimators when it comes to the state of multicollinearity.