Modifying estimators of ordered positive parameters under the Stein loss
Modifying estimators of ordered positive parameters under the Stein loss
复制标题
修改 Stein 损失下有序正参数的估计量
DOI：
10.1016/j.jmva.2010.08.011
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发表时间：
2011
影响因子：
1.6
通讯作者：
T.
中科院分区：
文献类型：
--
作者：
Tsukuma;H.;Kubokawa;T.
本文讨论了多面凸锥上正参数的估计问题，其中包括典型的序约束，如单序、树序和伞序约束。本文用两种方法证明了保序估计相对于不对底层分布作任何假设的粗糙非保序估计的改进。一种是利用Fenchel对偶定理，在多面体凸锥的一般约束下，证明了保序回归估计的优越性;另一种方法是利用Abel恒等式，我们可以得到一类改进的估计，其中包括在典型的顺序限制下基于顺序统计量的估计。当底层分布是尺度族时，证明了无偏估计及其阶限制估计是极小极大的。在二维情形下，证明了在有限空间上，广义贝叶斯估计对先验的极小极大性。最后给出了一些例子和多元扩展。
This paper treats the problem of estimating positive parameters restricted to a polyhedral convex cone which includes typical order restrictions, such as simple order, tree order and umbrella order restrictions. In this paper, two methods are used to show the improvement of order-preserving estimators over crude non-order-preserving estimators without any assumption on underlying distributions. One is to use Fenchel’s duality theorem, and then the superiority of the isotonic regression estimator is established under the general restriction to polyhedral convex cones. The use of the Abel identity is the other method, and we can derive a class of improved estimators which includes order-statistics-based estimators in the typical order restrictions. When the underlying distributions are scale families, the unbiased estimators and their order-restricted estimators are shown to be minimax. The minimaxity of the restrictedly generalized Bayes estimator against the prior over the restricted space is also demonstrated in the two dimensional case. Finally, some examples and multivariate extensions are given.