Estimation with Incompletely Specified Loss Functions (the Case of Several Location Parameters)
Estimation with Incompletely Specified Loss Functions (the Case of Several Location Parameters)
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DOI：
10.1080/01621459.1975.10479883
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发表时间：
1975-06
影响因子：
3.7
通讯作者：
L. Brown
中科院分区：
文献类型：
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作者：
L. Brown
摘要对于p ≥ 3个独立的正态均值的估计，如果p个独立的损失函数可以合并为一个损失函数，则通常的不变估计量是“不可接受的”。在这里，我们制定了一个版本的问题，损失不能以这种方式汇集，并找到了一个令人惊讶的弱的必要和充分条件下，通常的估计是不允许的，在某种意义上适当的制定。我们还研究了球对称的情况下，并找到一个不同的必要和充分条件。
Abstract If p ≥ 3 separate normal means are to be estimated, the usual, invariant estimator is “inadmissible” if the p separate loss functions can be pooled into a single loss function for the ensemble-of-means problem. Here, we formulate a version of the problem where the losses cannot be pooled in this way, and find a surprisingly weak necessary and sufficient condition under which the usual estimator is inadmissible in a sense appropriate to this formulation. We also examine the spherically symmetric case and find a different necessary and sufficient condition there.