摘要翻译：
我们考虑了估计与独立观测量相对应的n个参数向量的复合决策问题，并讨论了两类对称估计量之间的区别。第一类和更大的一类被限制为所有置换不变估计量的集合。第二类进一步限于简单的对称过程。也就是说，每个参数仅由相应观测的一个函数来估计的估计量。我们证明了在温和的条件下，这两类的最小总平方误差风险在本质上是渐近等价的O(1)差分。
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英文标题：
《Asymptotic efficiency of simple decisions for the compound decision
  problem》
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作者：
Eitan Greenshtein and Ya'acov Ritov
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  We consider the compound decision problem of estimating a vector of $n$ parameters, known up to a permutation, corresponding to $n$ independent observations, and discuss the difference between two symmetric classes of estimators. The first 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) difference.
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PDF链接：
https://arxiv.org/pdf/802.1319