Summary: The purpose of this paper is to investigate the optimality properties of the MSE of the principle component estimator in the class of reduced dimension estimators. It has been proved that the principle component estimator has the \(\mu\)-m, \(\mu\)-P income, loss and \(\mu\)-MB optimality properties. In addition, it has been proved that the principle component estimator is a general best Bayesian estimator of \(\beta\) in the class \({\mathcal D}_ r\).