Weak Versus Strong Dominance of Shrinkage Estimators

We consider the estimation of mean a multivariate normal distribution with known variance. Most studies risk competing estimators, that is trace squared error matrix. In contrast we whole matrix, in particular its eigenvalues. prove there are only two distinct eigenvalues and apply our findings to James–Stein Thompson class estimators. It turns out famous Stein paradox no longer when matrix rather than trace.