摘要翻译：
我们提出了一种鲁棒的方法来推断治疗变量对标量结果的影响，在有很多对照的情况下。我们的设置是一个部分线性模型，可能具有非高斯和异方差扰动。我们的分析允许控制的数量比样本量大得多。为了使信息推理可行，我们要求模型近似稀疏；也就是说，我们要求混杂因素的影响可以通过对相对较少数量的恒等式未知的控件的条件来控制到最小的近似误差。后一个条件使得通过选择近似正确的对照集来估计治疗效果成为可能。在此背景下，我们提出了一种新的治疗效果估计和一致有效的推断方法，称为“后双选择”方法。我们的结果适用于用于协变量选择的Lasso型方法，也适用于任何其他能够找到具有良好近似特性的稀疏模型的模型选择方法。我们的方法最吸引人的特点是，它允许不完全选择控制，并提供了在一大类模型中一致有效的置信区间。相比之下，标准的后模型选择估计器不能提供统一的推断，即使在简单的情况下，只有少量固定数量的控制。因此，我们的方法解决了对大量有趣的模型选择后的统一推理问题。我们用数值模拟和堕胎对犯罪率影响的应用说明了所开发方法的使用。
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英文标题：
《Inference on Treatment Effects After Selection Amongst High-Dimensional
  Controls》
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作者：
Alexandre Belloni and Victor Chernozhukov and Christian Hansen
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最新提交年份：
2012
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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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。
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一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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英文摘要：
  We propose robust methods for inference on the effect of a treatment variable on a scalar outcome in the presence of very many controls. Our setting is a partially linear model with possibly non-Gaussian and heteroscedastic disturbances. Our analysis allows the number of controls to be much larger than the sample size. To make informative inference feasible, we require the model to be approximately sparse; that is, we require that the effect of confounding factors can be controlled for up to a small approximation error by conditioning on a relatively small number of controls whose identities are unknown. The latter condition makes it possible to estimate the treatment effect by selecting approximately the right set of controls. We develop a novel estimation and uniformly valid inference method for the treatment effect in this setting, called the "post-double-selection" method. Our results apply to Lasso-type methods used for covariate selection as well as to any other model selection method that is able to find a sparse model with good approximation properties.   The main attractive feature of our method is that it allows for imperfect selection of the controls and provides confidence intervals that are valid uniformly across a large class of models. In contrast, standard post-model selection estimators fail to provide uniform inference even in simple cases with a small, fixed number of controls. Thus our method resolves the problem of uniform inference after model selection for a large, interesting class of models. We illustrate the use of the developed methods with numerical simulations and an application to the effect of abortion on crime rates.
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PDF链接：
https://arxiv.org/pdf/1201.0224