Improved minimax estimation of a multivariate normal mean under heteroscedasticity

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...

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

Ensemble Minimax Estimation for Multivariate Normal Means

This article discusses estimation of a heteroscedastic multivariate normal mean in terms of the ensemble risk. We first derive the ensemble minimaxity properties of various estimators that shrink towards zero. We then generalize our results to the case where the variances are given as a common unknown but estimable chi-squared random variable scaled by different known factors. We further provid...

On minimax estimation of a sparse normal mean vector

Mallows has conjectured that among distributions which are Gaussian but for occasional contamination by additive noise, the one having least Fisher information has (two-sided) geometric contamination. A very similar problem arises in estimation of a non-negative vector parameter in Gaussian white noise when it is known also that most, i.e. (1 − ǫ), components are zero. We provide a partial asym...

Optimal confidence interval for the largest normal mean under heteroscedasticity

A two-stage sampling procedure for obtaining an optimal confidence interval for the largest or smallest mean of k independent normal populations is proposed, where the population variances are unknown and possibly unequal. The optimal confidence interval is obtained by maximizing the coverage probability with a fixed width at a least favorable configuration of means. Then, the sample sizes can ...