Minimax Estimators of the Mean of a Multivariate Normal Distribution

Another Class of Minimax Estimators of A Variance Covariance Matrix in Multivariate Normal Distribution

It is well known that the best equivariant estimator of a variance covari-ance matrix of multivariate normal distribution with respect to the full ane group of transformation is not even minimax. Some minimax estimators have been proposed. Here we treat this problem in the framework of a multivari-ate analysis of variance(MANOVA) model and give other classes of minimax estimators.

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...

On combining correlated estimators of the common mean of a multivariate normal distribution

The inferential procedures based on an optimal combination of correlated estimators of the common mean of a multivariate normal distribution are considered. Exact properties of the conditional and unconditional confidence intervals due to Halperin [Halperin, 1961, Almost linearly-optimum combination of unbiased estimates. Journal of the American Statistical Association, 56, 36–43] are numerical...

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.

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