Ensemble Minimax Estimation for Multivariate Normal Means
Lawrence D. Brown, Hui Nie, Xianchao Xie · ScholarlyCommons (University of Pennsylvania) · 2011
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 provide a class of ensemble minimax estimators that shrink towards the common mean