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.
Scopus Subject Areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics
- Dimension reduction
- Heterogeneity treatment effects
- Propensity score