Second-Order Pitman Admissibility and Pitman Closeness: The Multiparameter Case and Stein-Rule Estimators

In a multiparameter estimation problem, for first-order efficient estimators, second-order Pitman admissibility, and Pitman closeness properties are studied. Bearing in mind the dominant role of Stein-rule estimators in multiparameter estimation theory, such second-order properties are also studied for shrinkage maximum likelihood estimators.