Abstract: A common problem in applied sciences is multicollinearity between variables. Multicollinearity is frequently encountered problems in practice that produce undesirable effects on classical Ordinary Least-Squares (OLS) regression estimator. The ridge estimation is an important tool to reduce the effects of multicollinearity. Also, it is suspected that some additional linear constraints may hold on to the whole parameter space. This restriction is based on either additional information or prior knowledge. The proposed estimators based on restricted estimator performs fairly well than the other estimators based on ordinary least-squares estimator. In this study, by some theorems, necessary and sufficient conditions for the superiority of the new estimator over the restricted least-squares estimator for selecting the ridge parameter k are derived. For illustrating the usefulness of the proposed result, the performance of this estimator is compared to the classic estimator via a simulation study in restricted partial linear regression models.