CIRJE-F-858 "Minimaxity in Estimation of Restricted and Non-restricted Scale Parameter Matrices"
Author Name

Tsukuma, Hisayuki and Tatsuya Kubokawa

Date September 2012
Full Paper   PDF file
Remarks  Forthcoming in Annals of the Institute of Statistical Mathematics.
Abstract
  In estimation of the normal covariance matrix, nding a least favorable sequence of prior distributions has been an open question for a long time. In this paper, we address the classical problem and succeed in construction of such a sequence, which establishes minimaxity of the best equivariant estimator. We also derive uni ed conditions for a sequence of prior distributions to be least favorable in the general estimation problem with an invariance structure. These uni ed conditions are applied to both restricted and non-restricted cases of parameters, and we give a couple of examples which show minimaxity of the best equivariant estimators under restrictions of the covariance matrix.