On Truncation of Shrinkage Estimators in Simultaneous Estimation of Normal Means
研究了在多元正态均值估计中，当均值可能来自重尾先验分布时，标准Stein估计量改进有限，而Stein提出的有限平移估计量能有效弥补这一缺陷，并分析了其自适应版本。
Abstract In estimating a multivariate normal mean θ = (θ1, …, θ k ) t under sum of squares error loss, it is well known that Stein estimators improve upon the usual estimator (in terms of expected loss) if k ≥ 3. The improvement obtained is significant, however, only if the θ i are fairly close to the point towards which the Stein estimator shrinks. When extreme θ i are likely (such as when the θ i are thought to arise from a possibly heavy-tailed prior distribution), the standard Stein estimators may offer little improvement over the usual estimator. Stein (1981) proposed a limited translation Stein estimator to correct this deficiency. This estimator is analyzed herein for a number of heavy-tailed prior distributions. An adaptive version of the estimator is also discussed.