I think I may have misinterpreted your original comment. It's true, as you say, that in the Stein estimator some individual MSEs get worse to yield a lower over

I think I may have misinterpreted your original comment. It's true, as you say, that in the Stein estimator some individual MSEs get worse to yield a lower overall MSE. I was focusing on your example and assuming you meant this was only possible because some individual MSEs were larger than others to begin with (under the individually optimal estimator).