On SURE-Type Double Shrinkage Estimation. Issue 516 (1st October 2016) - Jing, Bing-Yi; Li, Zhouping; Pan, Guangming; Zhou, Wang
ABSTRACT: The article is concerned with empirical Bayes shrinkage estimators for the heteroscedastic hierarchical normal model using Stein's unbiased estimate of risk (SURE). Recently, Xie, Kou, and Brown proposed a class of estimators for this type of problems and established their asymptotic optimality properties under the assumption of known but unequal variances. In this article, we consider this problem with unequal and unknown variances, which may be more appropriate in real situations. By placing priors for both means and variances, we propose novel SURE-type double shrinkage estimators that shrink both means and variances. Optimal properties for these estimators are derived under certain regularity conditions. Extensive simulation studies are conducted to compare the newly developed methods with other shrinkage techniques. Finally, the methods are applied to the well-known baseball dataset and a gene expression dataset. Supplementary materials for this article are available online.