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 <bold>y</bold>=<bold>X</bold> <bold>β</bold>+<bold>e</bold>. The problem arises if augmenting the equation <bold>0</bold>=<bold>c</bold>′<bold>α</bold>+<bold>ε</b old> instead of <bold>0</bold>=<bold>C</bold> <bold>α</bold>+<bold>ϵ</bold> 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.