Expansions for the risk of Stein type estimates for non-normal data

We consider the James–Stein problem for non-normal data for estimating a p-vector θ. It is shown how the risk may be expanded in powers of p-1. The factor 1-2/p that distinguishes the James–Stein estimate from the Stein estimate is shown to have only O(p-2) effect on the risk. The case, where the variance must be estimated is studied for the one-way unbalanced ANOVA problem.