论文标题
具有仪器变量的局部平均治疗效果的高维模型辅助推断
High-dimensional Model-assisted Inference for Local Average Treatment Effects with Instrumental Variables
论文作者
论文摘要
考虑使用仪器变量估算局部平均治疗效果的问题，在调整一组测得的协变量后，仪器不符。需要通过回归模型来估算协变量的几个未知功能，例如仪器倾向得分和治疗以及结果回归模型。我们在高维设置中开发了一种可计算方法的方法，其中回归项的数量接近或大于样本量。我们的方法利用了正则校准估计，该估计涉及套件惩罚，但精心选择的损失函数来估计这些回归模型中系数向量，然后通过增强的相反概率加权使用双重强大的估计器来用于处理参数。我们提供严格的理论分析，以表明如果正确指定了仪器倾向分数模型，则在适当的稀疏条件下所产生的WALD置信区间对治疗参数有效，但是处理和结果回归模型可能会被弄清楚。对于现有的高维方法，如果正确指定了所有三个模型，则将获得治疗参数的有效置信区间。我们通过广泛的模拟研究和经验应用来评估所提出的方法，以估算教育的回报。
Consider the problem of estimating the local average treatment effect with an instrument variable, where the instrument unconfoundedness holds after adjusting for a set of measured covariates. Several unknown functions of the covariates need to be estimated through regression models, such as instrument propensity score and treatment and outcome regression models. We develop a computationally tractable method in high-dimensional settings where the numbers of regression terms are close to or larger than the sample size. Our method exploits regularized calibrated estimation, which involves Lasso penalties but carefully chosen loss functions for estimating coefficient vectors in these regression models, and then employs a doubly robust estimator for the treatment parameter through augmented inverse probability weighting. We provide rigorous theoretical analysis to show that the resulting Wald confidence intervals are valid for the treatment parameter under suitable sparsity conditions if the instrument propensity score model is correctly specified, but the treatment and outcome regression models may be misspecified. For existing high-dimensional methods, valid confidence intervals are obtained for the treatment parameter if all three models are correctly specified. We evaluate the proposed methods via extensive simulation studies and an empirical application to estimate the returns to education.
