Two sufficient conditions for characterizing Pitman nearness (PN) are derived. It is found that one of the conditions is a standardized decision criterion. Two examples are given, including comparison of the James-Stein estimator with the usual unbiased estimator. It is also shown that stochastic domination implies PN for comparing any two multivariate normal estimators. Moreover, they are equivalent if two estimators are unbiased.
- James-Stein estimator
- Pitman nearness
- generalized squared-error loss
- stochastic domination