Multivariate limited translation estimators

Bayes estimators are used quite often in the theory and practice of statistics. Their popularity is attributed to the more efficient inference that they often lead to compared to classical frequentist procedures. However, the Bayes estimators can result in high Bayes risk when the prior distribution is misspecified. Additionally, they can result in high frequentist risk when they are used for estimating parameters which depart widely from the assumed prior means.; We developed multivariate limited translation Bayes estimators of the normal mean vector which serve as a compromise between the Bayes and the maximum likelihood estimators. We demonstrated the superiority of the limited translation estimators over the usual Bayes estimators under misspecified priors and often also in terms of the frequentist risks under the situation stated in the previous paragraph.; We also extended the above results and developed multivariate limited translation empirical Bayes estimators of the normal mean vector which serve as a compromise between the empirical Bayes estimators and the maximum likelihood estimators. These compromise estimators perform better than the regular empirical Bayes estimators, in a frequentist sense, when there is wide departure of an individual observation from the grand average.