A new perspective on dominating the James-Stein estimator

Abstract: This paper presents a novel approach to constructing estimators that dominate the classical James-Stein estimator under the quadratic loss for multivariate normal means. Building on Stein's risk representation, we introduce a new sufficient condition involving a monotonicity property of a transformed shrinkage function. We derive a general class of shrinkage estimators that satisfy minimaxity and dominance over the James-Stein estimator, including cases with polynomial or logarithmic convergence to the optimal shrinkage factor. We also provide conditions for uniform dominance across dimensions and for improved asymptotic risk performance. We present several examples and numerical validations to illustrate the theoretical results.