Generalizations of James-Stein Estimators Under Spherical Symmetry
Generalizations of James-Stein Estimators Under Spherical Symmetry
复制标题
球对称下 James-Stein 估计量的推广
DOI：
10.1214/aos/1176348267
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发表时间：
1991
影响因子：
--
通讯作者：
W. Strawderman
中科院分区：
文献类型：
--
作者：
A. Brandwein;W. Strawderman
本文主要是将Stein的结果推广到球对称分布。当X = f（||X - θ|| 2），我们研究了损失函数的估计量X ag（X）优于X的条件||δ- θ|| 2和损失函数是凹的，||δ- θ|| 2.此外，如果规模是未知的，我们调查的位置参数的形式X aVg（X）在两个不同的设置的估计。在第一种情况下，尺度的估计量V与X无关。在第二种情况下，V是从球对称分布采样时广义线性模型的通常规范设置中的残差平方和。这些结果也被推广到凹损失。控制X ag（X）的条件通常是（a）||G|| 2 2 g ≤0，（B）2 2 g是超调和的，（c）0
This paper is primarily concerned with extending the results of Stein to spherically symmetric distributions. Specifically, when X ∼f(||X - θ||2), we investigate conditions under which estimators of the form X ag(X) dominate X for loss functions ||δ- θ||2 and loss functions which are concave in ||δ- θ||2. Additionally, if the scale is unknown we investigate estimators of the location parameter of the form X aVg(X) in two different settings. In the first, an estimator V of the scale is independent of X. In the second, V is the sum of squared residuals in the usual canonical setting of a generalized linear model when sampling from a spherically symmetric distribution. These results are also generalized to concave loss. The conditions for domination of X ag(X) are typically (a) ||g||2 2∇∘g ≤0, (b) ∇∘g is superharmonic and (c) 0