This article discusses estimation of a multivariate normal mean based on heteroscedastic observations. Under heteroscedasticity, estimators shrinking more on the coordinates with larger variances, seem desirable. Although they are not necessarily minimax in the ordinary sense, we show that such James-Stein type estimators can be ensemble minimax, minimax with respect to the ensemble risk, related to empirical Bayes perspective of Efron and Morris.

翻译：本篇文章讨论基于异性观察的多变正常平均值的估计。 在异性观察下,估计值在坐标上缩小得更多,且差异较大,这似乎是可取的。 虽然它们不一定是普通意义上的最小值,但我们表明,这些詹姆斯-斯丁类估计值可以是混合的微型最大值,与埃弗伦和莫里斯的经验型海湾观点相关的共同风险微值。