摘要翻译：
本文研究了治疗分配问题的一个惩罚统计决策规则。考虑一个功利主义政策制定者的设置，他必须使用样本数据，根据人口的可观察特征，为其成员分配二元处理。我们将此问题建模为一个统计决策问题，其中决策者必须从一类潜在子集中选择协变量空间的一个子集来分配处理。我们将重点放在策略制定者可能想要在约束子集类集合中进行选择的设置上：示例包括选择执行最佳子集选择的协变量的数量，以及通过筛选近似复杂类时的模型选择。我们采用并扩展了统计学习的结果来发展惩罚福利最大化(PWM)规则。我们针对PWM规则的缺陷建立了一个oracle不等式，表明它能够在可用类集合上进行模型选择。然后我们用这个oracle不等式推导出PWM最大遗憾的相关界。我们的结果的一个重要结果是，我们能够使用“保持”过程来形式化模型选择，在这种过程中，政策制定者首先使用一半的数据来估计各种政策，然后选择在对另一半数据进行评估时表现最好的政策。
---
英文标题：
《Model Selection for Treatment Choice: Penalized Welfare Maximization》
---
作者：
Eric Mbakop and Max Tabord-Meehan
---
最新提交年份：
2020
---
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
--
一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
--
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。
--

---
英文摘要：
  This paper studies a penalized statistical decision rule for the treatment assignment problem. Consider the setting of a utilitarian policy maker who must use sample data to allocate a binary treatment to members of a population, based on their observable characteristics. We model this problem as a statistical decision problem where the policy maker must choose a subset of the covariate space to assign to treatment, out of a class of potential subsets. We focus on settings in which the policy maker may want to select amongst a collection of constrained subset classes: examples include choosing the number of covariates over which to perform best-subset selection, and model selection when approximating a complicated class via a sieve. We adapt and extend results from statistical learning to develop the Penalized Welfare Maximization (PWM) rule. We establish an oracle inequality for the regret of the PWM rule which shows that it is able to perform model selection over the collection of available classes. We then use this oracle inequality to derive relevant bounds on maximum regret for PWM. An important consequence of our results is that we are able to formalize model-selection using a "hold-out" procedure, where the policy maker would first estimate various policies using half of the data, and then select the policy which performs the best when evaluated on the other half of the data.
---
PDF链接：
https://arxiv.org/pdf/1609.03167