A novel unified linear biased estimator

A novel unified biased estimator based on the linear transform matrix acting on the least-squares estimator (LSE) in canonical form is proposed for coping with multicollinearity problem and its properties are also discussed in this paper. We show that our new biased estimator is superior, in the mean squared error (MSE) sense, to the LSE. Ridge estimator, Liu estimator, etc. are viewed as a subclass of the class of the proposed estimator which is the linear transform of LSE. Finally, a numerical example widely used in the literatures is studies based on Monte Carlo simulation to show the behavior of the different estimators.