Semiparametric efficient estimation of various multi-valued causal effects, including quantile treatment effects, is important in economic, biomedical, and other social sciences. Under the unconfoundedness condition, adjustment for confounders requires estimating the nuisance functions relating outcome or treatment to confounders nonparametrically. This paper considers a generalized optimization framework for efficient estimation of general treatment effects using artificial neural networks (ANNs) to approximate the unknown nuisance function of growing-dimensional confounders. We establish a new approximation error bound for the ANNs to the nuisance function belonging to a mixed smoothness class without a known sparsity structure. We show that the ANNs can alleviate the "curse of dimensionality" under this circumstance. We establish the root-$n$ consistency and asymptotic normality of the proposed general 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：半参数有效估计多种多值处理效应（包括分位数处理效应）在经济、生物医学及其他社会科学领域具有重要意义。在无混杂假设下，混杂因素调整需要非参数地估计与结果或处理相关的干扰函数。本文提出一个广义优化框架，利用人工神经网络逼近未知且维数递增的混杂因素干扰函数，以实现一般处理效应的有效估计。我们建立了一个新的近似误差界，该界适用于属于混合光滑性类别且无需已知稀疏结构的干扰函数的神经网络逼近。研究表明，在此情况下神经网络可缓解“维度灾难”。我们证明了所提出的一般处理效应估计量的根号$n$一致性与渐近正态性，并采用加权自助法进行统计推断。通过模拟研究与真实数据应用对所提方法进行了验证。