Best linear estimation via minimization of relative mean squared error

Abstract

We propose methods to construct a biased linear estimator for linear regression which optimizes the relative mean squared error (MSE). Although there have been proposed biased estimators which are shown to have smaller MSE than the ordinary least squares estimator, our construction is based on the minimization of relative MSE directly. The performance of the proposed methods is illustrated by a simulation study and a real data example. The results show that our methods can improve on MSE, particularly when there exists correlation among the predictors.