Ai et al. (2021) studied the estimation of a general dose-response function (GDRF) of a continuous treatment that includes the average dose-response function, the quantile dose-response function, and other expectiles of the dose-response distribution. They specified the GDRF as a parametric function of the treatment status only and proposed a weighted regression with the weighting function estimated using the maximum entropy approach. This paper specifies the GDRF as a nonparametric function of the treatment status, proposes a weighted local linear regression for estimating GDRF, and develops a bootstrap procedure for constructing the uniform confidence bands. We propose stable weights with minimum sample variance while eliminating the sample association between the treatment and the confounding variables. The proposed weights admit a closed-form expression, allowing them to be computed efficiently in the bootstrap sampling. Under certain conditions, we derive the uniform Bahadur representation for the proposed estimator of GDRF and establish the validity of the corresponding uniform confidence bands. A fully data-driven approach to choosing the undersmooth tuning parameters and a data-driven bias-control confidence band are included. A simulation study and an application demonstrate the usefulness of the proposed approach.

翻译：Ai等人（2021）研究了包含平均剂量-响应函数、分位数剂量-响应函数以及剂量-响应分布其他期望在内的通用连续处理剂量-响应函数（GDRF）的估计问题。他们将GDRF仅设定为处理状态的参数函数，并提出了使用最大熵方法估计权重函数的加权回归。本文则将GDRF设定为处理状态的非参数函数，提出了用于估计GDRF的加权局部线性回归方法，并开发了用于构建统一置信带的Bootstrap程序。我们提出了具有最小样本方差、同时能消除处理与混杂变量间样本关联的稳定权重。所提出的权重具有闭式表达式，使其能够在Bootstrap抽样中被高效计算。在一定条件下，我们推导了所提GDRF估计量的统一Bahadur表示，并建立了相应统一置信带的有效性。文中包含了选择欠光滑调优参数的完全数据驱动方法以及数据驱动的偏差控制置信带。模拟研究和一项应用证明了所提方法的有效性。