Minimax estimation of normal precisions via expansion estimators

In this paper, the simultaneous estimation of the precision parameters of k normal distributions is considered under the squared loss function in a decision-theoretic framework. Several classes of minimax estimators are derived by using the chi-square identity, and the generalized Bayes minimax estimators are developed out of the classes. It is also shown that the improvement on the unbiased estimators is characterized by the superharmonic function. This corresponds to Stein's [1981. Estimation of the mean of a multivariate normal distribution. Ann. Statist. 9, 1135–1151] result in simultaneous estimation of normal means.