The research in this paper gives a systematic investigation of the asymptotic behaviors of four inverse probability weighting (IPW)-based estimators for conditional average treatment effects, with nonparametrically, semiparametrically, parametrically estimated, and true propensity score, respectively. To this end, we first pay particular attention to semiparametric dimension reduction structure such that we can study the semiparametric-based estimator that can alleviate the curse of dimensionality and greatly avoid model misspecification. We also derive some further properties of the existing estimator with a nonparametrically estimated propensity score. According to their asymptotic variance functions, the studies reveal the general ranking of their asymptotic efficiencies; in which scenarios the asymptotic equivalence can hold; the critical roles of the affiliation of the given covariates in the set of arguments of the propensity score, the bandwidth and kernel function selections. The results show an essential difference from the IPW-based estimator of the unconditional average treatment effects(ATE). The numerical studies indicate that for high-dimensional paradigms, the semiparametric-based estimator performs well in general whereas the nonparametric-based estimator, even sometimes parametric-based estimator, is more susceptible to dimensionality. Some numerical studies are carried out to examine their performance. A real data example is analyzed for illustration.

本文的研究对有条件平均治疗效果的四个基于逆概率加权（IPW）的估计量的渐近行为进行了系统的研究，分别具有非参数，半参数，参数估计和真实倾向得分。为此，我们首先要特别注意半参数降维结构，以便我们可以研究基于半参数的估计器，该估计器可以减轻维数的诅咒并大大避免模型错误指定。我们还用非参数估计的倾向得分推导了现有估计量的其他一些属性。根据他们的渐近方差函数，研究揭示了他们的渐近效率的一般排名。在什么情况下可以保持渐近等价；给定协变量的从属关系在倾向得分，带宽和核函数选择的参数集中的关键作用。结果表明，与基于IPW的估计器的无条件平均治疗效果（ATE）有本质区别。数值研究表明，对于高维范式，基于半参数的估计量通常表现良好，而基于非参数的估计量，甚至有时基于参数的估计量，对维度的敏感性更高。进行了一些数值研究以检查其性能。分析一个真实的数据示例以进行说明。结果表明，与基于IPW的估计器的无条件平均治疗效果（ATE）有本质区别。数值研究表明，对于高维范例，基于半参数的估计量总体上表现良好，而基于非参数的估计量，甚至有时基于参数的估计量，对维度的敏感性更高。进行了一些数值研究以检查其性能。分析一个真实的数据示例以进行说明。结果表明，与基于IPW的估计器的无条件平均治疗效果（ATE）有本质区别。数值研究表明，对于高维范式，基于半参数的估计量通常表现良好，而基于非参数的估计量，甚至有时基于参数的估计量，对维度的敏感性更高。进行了一些数值研究以检查其性能。分析一个真实的数据示例以进行说明。进行了一些数值研究以检查其性能。分析一个真实的数据示例以进行说明。进行了一些数值研究以检查其性能。分析一个真实的数据示例以进行说明。