Estimation of the mean vector of a multivariate normal distribution under symmetry

摘要

Da Silva and Han (1984) considered preliminary test estimation (PTE) of the mean vector of ap-variate normal distribution with unknown covariance matrix when it isa priorisuspected that the component means are equal but unknown. In this paper, six possible estimators are considered, namely, the unrestricted maximum likelihood estimator (UMLE), the restricted MLE (RMLE), the preliminary test MLE (PTMLE), the modified PTMLE (MPTMLE), the shrinkage MLE (SMLE), and the positive-rule shrinkage MLE (PRSMLE) under more general setting. The comparative properties of the estimators are studied with respect to a specific quadratic loss function using special covariance structure. It is shown that neither PTMLE nor SMLE dominate each other, though they fare well compared to UMLE and RMLE.