MSE dominance of the positive-part shrinkage estimator when each individual regression coefficient is estimated

In this paper we consider a regression model and a general family of shrinkage estimators of regression coefficients. The estimation of each individual regression coefficient is important in some practical situations. Thus, we derive the formula for the mean squared error (MSE) of the general class of shrinkage estimators for each individual regression coefficient. It is shown analytically that the general family of shrinkage estimators is dominated by its positive-part variant in terms of MSE whenever there exists the positive-part variant or, in other words, the shrinkage factor can be negative for some parameter and data values. Copyright Springer-Verlag Berlin Heidelberg 2015