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摘要翻译：
在本文中，我们研究了聚合问题，它可以表述如下。假设我们有一族估计量$\mathcal{F}$建立在可用观测的基础上。目标是构造一个新的估计量，其风险尽可能接近于家族中最佳估计量的风险。我们提出了一个通用的聚合方案，该方案在以下意义上是通用的：它适用于任意估计量族、各种模型和全局风险度量。这个过程是基于对某些线性函数的经验估计与由$\Mathcal{F}$族导出的估计的比较。我们导出了oracle不等式，并证明了它们在某种意义上是不可改进的。数值结果表明该方法具有良好的实用性能。
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英文标题：
《A universal procedure for aggregating estimators》
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作者：
Alexander Goldenshluger
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最新提交年份：
2009
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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：
In this paper we study the aggregation problem that can be formulated as follows. Assume that we have a family of estimators $\mathcal{F}$ built on the basis of available observations. The goal is to construct a new estimator whose risk is as close as possible to that of the best estimator in the family. We propose a general aggregation scheme that is universal in the following sense: it applies for families of arbitrary estimators and a wide variety of models and global risk measures. The procedure is based on comparison of empirical estimates of certain linear functionals with estimates induced by the family $\mathcal{F}$. We derive oracle inequalities and show that they are unimprovable in some sense. Numerical results demonstrate good practical behavior of the procedure.
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PDF链接：
https://arxiv.org/pdf/704.25
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