  In this article we provide some nonnegative and positive estimators of the
mean squared errors(MSEs) for shrinkage estimators of multivariate normal
means. Proposed estimators are shown to improve on the uniformly minimum
variance unbiased estimator(UMVUE) under a quadratic loss criterion. A similar
improvement is also obtained for the estimators of the MSE matrices for
shrinkage estimators. We also apply the proposed estimators of the MSE matrix
to form confidence sets centered at shrinkage estimators and show their
usefulness through numerical experiments.
