An Explicit Formula for the Risk of the Positive-Part James-Stein Estimator

When estimating a normal mean vector with variance known up to a multiplicative factor, it is well known that the positive-part James-Stein estimator is not admissible, but until now, no one has been able to exhibit a uniformly better estimator. We propose here an explicit formula for the risk of the positive-part James-Stein estimator.