Outcome regression-based estimation of conditional average treatment effect

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 corresponding asymptotic variance functions when supposing models are correctly specified, answer questions: what efficiency ranking four in general? how related affiliation of given covariates set arguments regression functions? do roles bandwidth kernel function selections play estimation efficiency; which scenarios should estimator under structure be used practice? Meanwhile, results show that any asymptotically more efficient than inverse probability weighting-based estimation. Several simulation studies conducted examine finite sample performances these estimators, real dataset analyzed illustration.