The research is about a systematic investigation on the following issues. First, we construct different outcome regression-based estimators for conditional average treatment effect under, respectively, true, parametric, nonparametric and semiparametric dimension reduction structure. Second, according to the corresponding asymptotic variance functions when supposing the models are correctly specified, we answer the following questions: what is the asymptotic efficiency ranking about the four estimators in general? how is the efficiency related to the affiliation of the given covariates in the set of arguments of the regression functions? what do the roles of bandwidth and kernel function selections play for the estimation efficiency; and in which scenarios should the estimator under semiparametric dimension reduction regression structure be used in practice? Meanwhile, the results show that any outcome regression-based estimation should be asymptotically more efficient than any inverse probability weighting-based estimation. Several simulation studies are conducted to examine the finite sample performances of these estimators, and a real dataset is analyzed for illustration.

该研究是对以下问题的系统调查。首先，我们分别在真实、参数、非参数和半参数降维结构下为条件平均治疗效果构建了不同的基于结果回归的估计量。其次，在假设模型正确指定的情况下，根据相应的渐近方差函数，我们回答以下问题：四个估计量的渐近效率排序一般是多少？效率如何与回归函数的参数集中给定协变量的隶属关系相关？带宽和核函数选择对估计效率有何影响；以及在实践中应该在哪些场景下使用半参数降维回归结构下的估计器？同时，结果表明，任何基于结果回归的估计都应该比任何基于逆概率加权的估计更有效。进行了几项模拟研究来检查这些估计器的有限样本性能，并分析了一个真实的数据集以进行说明。