The estimation of causal effects is a primary goal of behavioral, social, economic and biomedical sciences. Under the unconfoundedness condition, adjustment for confounders requires estimating the nuisance functions relating outcome and/or treatment to confounders. This paper considers a generalized optimization framework for efficient estimation of general treatment effects using feedforward artificial neural networks (ANNs) when the number of covariates is allowed to increase with the sample size. We estimate the nuisance function by ANNs, and develop a new approximation error bound for the ANNs approximators when the nuisance function belongs to a mixed Sobolev space. We show that the ANNs can alleviate the curse of dimensionality under this circumstance. We further establish the consistency and asymptotic normality of the proposed treatment effects estimators, and apply a weighted bootstrap procedure for conducting inference. The proposed methods are illustrated via simulation studies and a real data application.

翻译：因果效应的估计是行为科学、社会科学、经济学和生物医学领域的主要目标。在无混杂假设条件下，通过混杂变量调整需要估计与结果和/或治疗相关的扰动函数。本文考虑一个通用优化框架，当协变量数量允许随样本量增加时，利用前馈人工神经网络（ANNs）高效估计通用治疗效果。我们通过ANNs估计扰动函数，并针对该函数属于混合Sobolev空间的情形，为ANNs近似器建立了新的逼近误差界。研究表明，在此条件下ANNs能够缓解维度灾难。我们进一步证明了所提出的治疗效果估计量的一致性及渐近正态性，并采用加权自助法进行推断。通过模拟研究和实际数据应用展示了所提方法的有效性。