Estimating Risk and the Mean Squared Error Matrix in Stein Estimation

It is well known that the uniformly minimum variance unbiased (UMVU) estimators of the risk and the mean squared error (MSE) matrix proposed in the literature for Stein estimators can take negative values with positive probability. In this paper, improved truncated estimators of the risk, risk difference, and MSE matrix are proposed and shown to be better than the UMVU estimators in terms of mean squared error.