Stein's Estimation Rule and Its Competitors- An Empirical Bayes Approach
Stein's Estimation Rule and Its Competitors- An Empirical Bayes Approach
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DOI：
10.1080/01621459.1973.10481350
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发表时间：
1973-03
影响因子：
3.7
通讯作者：
B. Efron;C. Morris
中科院分区：
文献类型：
--
作者：
B. Efron;C. Morris
当k≥3时，k正态均值的Stein估计量支配MLE。在这篇文章中，我们将探讨Stein的估计量是否有其自身的优点。我们的答案是肯定的：Stein估计量的正部分版本是一类“好”规则的一个成员，这些规则具有贝叶斯性质，也支配着MLE。这个类的其他成员在各种情况下也很有用。我们的方法是通过经验贝叶斯思想。在后面的章节中，我们将讨论更复杂的估计问题的规则，并以非正态情况下的经验线性贝叶斯规则的结果作为结论。
Abstract Stein's estimator for k normal means is known to dominate the MLE if k ≥ 3. In this article we ask if Stein's estimator is any good in its own right. Our answer is yes: the positive part version of Stein's estimator is one member of a class of “good” rules that have Bayesian properties and also dominate the MLE. Other members of this class are also useful in various situations. Our approach is by means of empirical Bayes ideas. In the later sections we discuss rules for more complicated estimation problems, and conclude with results from empirical linear Bayes rules in non-normal cases.