Comparison of restricted and unrestricted estimators in the multiple linear regression analysis

This thesis deals with the problem of multicollinearity in the linear regression model. In both classical and restricted linear regression models, when the least squares (LS) method is employed in the presence of multicollinearity, parameter estimates are unstable and have a high variance. In this case, to avoid the negative effects of multicollinearity over the LS it is recommended to use alternative biased estimators instead. In this thesis, Ridge, Contraction, Liu, Two-parameter, Restricted ridge, Restricted contraction, Restricted Liu, and Restricted two-parameter estimators were 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 was compared according to matrix mean square error and scalar mean square error. In this study, applications were made with two real data sets known in the literature in order to show which of the estimators had better performance in the light of the theories previously discussed in the literature. These analyses are based on Portland cement data and total national research and development expenditures data using the MATLAB program. In addition to these applications with real data sets, the results obtained are also detailed with a Monte-Carlo simulation study. As a result, it was decided that the most effective estimators are the restricted biased estimators when it comes to the state of multicollinearity.