Multicollinearity in regression analysis: Parametric and semiparametric estimation

Multicollinearity is a statistical phenomenon in which two or more predictor variables in a multiple regression model have a nearly linear relation. In this situation the coefficient estimates may change erratically in response to small changes in the data. Multicollinearity seriously affects calculations regarding individual predictors. That is, a multiple regression model with correlated predictors may give invalid results about any individual predictor; therefore it is a phenomenon that should be considered carefully. There have been many attempts in literature as a remedy to multicollinearity problem. The main stream approach is using biased estimators in place of ordinary least squares (OLS) estimators. It is well known that biased estimators are more efficient than OLS estimators in case of multicollinearity. In this study, new biased estimators are proposed for parametric or semiparametric regression models that are exposed to multicollinearity problem. The mean squared error matrix (MSEM) superiority conditions are given for each estimator. Theoretical findings are supported with applications and simulation studies.