On minimaxity and limit of risks ratio of james-stein estimator under the balanced loss function

The problem of estimating the mean of a multivariate normal distribu-tion by different types of shrinkage estimators is investigated. Under the balanced loss function, we establish the minimaxity of the James-Stein estimator. When the dimension of the parameters space and the sample size tend to infinity, we study the asymptotic behavior of risks ratio of James-Stein estimator to the maximum likelihood estimator. The positive-part of James-Stein estimator is also treated.