Inference on Treatment Effects After Selection Amongst High-Dimensional Controls
高维控制变量选择后的处理效应推断AI 解读 ↓
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高维控制变量选择后的处理效应推断
- 研究问题
- 在控制变量数量远超样本量且选择可能出错时，如何在部分线性模型中估计处理效应，并构造统一有效的置信区间？
- 方法与思路
- 作者在近似稀疏设定下提出选择后双重选择方法，允许非高斯与异方差误差，并涵盖能找到良好稀疏近似的选择程序。
- 材料陈述的贡献
- 摘要称该方法容许不完美控制变量选择，并在较大模型类上实现统一有效推断；模拟及堕胎与犯罪率应用用于展示。
- 阅读关注点
- 应核对双重选择的具体步骤、混杂控制与近似误差条件，以及统一有效性涵盖的模型类和其他选择方法的要求。
- 阅读边界
- 这是 arXiv 预印本，不能据此确认同行评审或期刊接收；摘要未完整说明因果识别条件，统一有效性仍依赖指定模型类。
原文摘要
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.