On characterizations of pitman closeness of some shrinkage estimators

Abstract

For the multivariate normal mean (vector) estimation problem, some characterizations of the Pitman closest property of a general class of shrinkage (or Stein-rule) estimators (including the so called positive-rule versions) are studied. Further, for the same model when the parameter is restricted to a positively homogeneous cone, Pitman closeness of restricted shrinkage maximum likelihood estimators is established.

Keywords:

• Pitman closest estimator
• positive-rule version
• positively homogeneous cone
• quadratic loss
• restricted MLE
• transitiueness