The exact general formulae for the moments and the MSE dominance of the Stein-rule and positive-part Stein-rule estimators

In this paper, we derive the general formulae for the moments of a linear functional of the Stein-rule and positive-part Stein-rule estimators (i.e., h′bSR and h′bPSR) in a different way from Phillips (1984). The MSE dominance of h′bPSR over h′bSR and a sufficient condition for h′bSR to dominate a linear functional of the OLS estimator (h′b) are shown. Using the formulae for the moments, we evaluate numerically the first four moments of bSR and bPSR, and examine the bias, variance, MSE, skewness, and kurtosis.