Component risk in multiparameter estimation

Summary For estimating the mean of ap-variate normal distribution under a quadratic loss, a class of estimators, known as Stein's estimators, is known to dominate the maximum likelihood estimator (MLE) forp≧3. But, whereas the risk of the MLE has the same value, equal to a constant, for each component, the maximum component risk of Stein's estimator is large for large values ofp. Certain modification of Stein's rule has been proposed in the literature for reducing the maximum component risk. In this paper, a new rule is given for reducing the maximum component risk. The new rule yields larger reduction in the maximum component risk, compared to its competitor.