Epsilon-Dominating Component-Wise Shrinkage Estimators of Normal Mean

Abstract

In this chapter we investigate the effect of an improved component-wise estimation of the expectation vectors for normal vectors with independent components. The dimension of variables and the sample size are supposed to be sufficiently high to apply the technique of singling out the leading terms in the asymptotics of the increasing dimension. But we will not pass to the limit and will obtain relations valid for any chosen dimension and any chosen sample size along with upper estimates of the remainder terms accurate up to absolute constants.