You probably wouldn't expect them to. But the same kind of Stein phenomenon holds under a much broader set of conditions, including arbitrary covariance matrice

You probably wouldn't expect them to. But the same kind of Stein phenomenon holds under a much broader set of conditions, including arbitrary covariance matrices and arbitrary quadratic loss, (see e.g. [1]). It's a very general phenomenon! [1] https://projecteuclid.org/euclid.aos/1176345691 https://projecteuclid.org/euclid.aos/1176345691