Improved ridge estimators in a linear regression model

In this paper, the notion of the improved ridge estimator (IRE) is put forward in the linear regression model y = Xβ + e. The problem arises if augmenting the equation 0 = c α + instead of 0 = Cα + ε to the model. Three special IREs are considered and studied under the mean-squared error criterion and the prediction error sum of squares criterion. The simulations demonstrate that the proposed estimators are effective and recommendable, especially when multicollinearity is severe.