Asymptotic e-ciency of simple decisions for the compound decision problem ⁄
Asymptotic e-ciency of simple decisions for the compound decision problem ⁄
复制标题
复合决策问题的简单决策的渐近效率 ⁄
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Y. Ritov
中科院分区：
文献类型：
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作者：
E. Greenshtein;Y. Ritov
本文考虑了估计一个由n个参数组成的向量的复合决策问题，该向量对应于n个独立的观测值，且已知一个置换，并讨论了两类对称估计量之间的区别。第一个和更大的类被限制为所有置换不变估计的集合。第二类进一步限制为简单的对称过程。也就是说，估计器使得每个参数仅由相应观测值的函数估计。我们证明了，在温和的条件下，这两个类的最小总平方误差风险是渐近等价的，直到本质上O（1）的差异。AMS 2000科目分类：小学62 C25;中学62 C12、62 C 07。
We consider the compound decision problem of estimating a vector of n parameters, known up to a permutation, corresponding to n in- dependent observations, and discuss the difierence between two symmetric classes of estimators. The flrst and larger class is restricted to the set of all permutation invariant estimators. The second class is restricted further to simple symmetric procedures. That is, estimators such that each parameter is estimated by a function of the corresponding observation alone. We show that under mild conditions, the minimal total squared error risks over these two classes are asymptotically equivalent up to essentially O(1) difierence. AMS 2000 subject classiflcations: Primary 62C25; secondary 62C12, 62C07.