Proper Bayes Minimax Estimators of the Multivariate Normal Mean

Improved minimax estimation of a multivariate normal mean under heteroscedasticity

Consider the problem of estimating a multivariate normal mean with a known variance matrix, which is not necessarily proportional to the identity matrix. The coordinates are shrunk directly in proportion to their variances in Efron and Morris’ (J. Amer. Statist. Assoc. 68 (1973) 117–130) empirical Bayes approach, whereas inversely in proportion to their variances in Berger’s (Ann. Statist. 4 (1...

Combining Multivariate Estimators of the Mean Vector

Meta-analysis is a standard statistical method used to combine the conclusions of individual studies that are related and the results of single study alone can not answered to deal with issues. The data are summarized by one or more outcome measure estimates along with their standard errors. The multivariate model and the variations between studies are not considered in most articles. Here we d...

Minimax estimators of a normal variance

In the estimation problem of unknown variance of a multivariate normal distribution, a new class of minimax estimators is obtained. It is noted that a sequence of estimators in our class converges to the Stein’s truncated estimator.

Multivariate limited translation hierarchical Bayes estimators

Based on the notion of predictive influence functions, the paper develops multivariate limited translation hierarchical Bayes estimators of the normal mean vector which serve as a compromise between the hierarchical Bayes and maximum likelihood estimators. The paper demonstrates the superiority of the limited translation estimators over the usual hierarchical Bayes estimators in terms of the fr...

Estimation of the Multivariate Normal Mean under the Extended Reflected Normal Loss Function