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：对因果关系的估计是行为、社会、经济和生物医学科学的首要目标。在缺乏依据的情况下,调整混乱者需要估计与结果和/或治疗有关的干扰功能,以便向混乱者提供治疗。本文件审议了一个普遍优化框架,以便利用饲料向前人工神经网络(ANNs)有效估计一般治疗效应,因为允许同化体数量随着样本规模的增加而增加。我们估算了非本国国民的干扰功能,并在骚扰功能属于混合的索博列夫空间时,为非本国国民的近似差出一个新的差错。我们表明,非本国国民可以减轻这种情况下对维度的诅咒。我们进一步确定拟议的治疗效应估计器的一致性和无损常性,并采用加权制导程序进行推理。通过模拟研究和真实数据应用来说明拟议的方法。