On IPW-based estimation of conditional average treatment effect

TL;DR

This paper systematically investigates the asymptotic behaviors of four IPW-based estimators for conditional average treatment effect, highlighting the advantages of semiparametric methods in high-dimensional settings and providing theoretical and numerical insights.

Contribution

It introduces a semiparametric dimension reduction approach for IPW estimators, improving efficiency and robustness in high-dimensional covariate spaces.

Findings

Semiparametric estimator outperforms nonparametric and parametric estimators in high dimensions.

Asymptotic efficiency depends on covariate structure, bandwidth, and kernel choices.

Numerical studies confirm the theoretical advantages of semiparametric methods.

Abstract

The research in this paper gives a systematic investigation on the asymptotic behaviours of four inverse probability weighting (IPW)-based estimators for conditional average treatment effect, with nonparametrically, semiparametrically, parametrically estimated and true propensity score, respectively. To this end, we first pay a particular attention to semiparametric dimension reduction structure such that we can well study the semiparametric-based estimator that can well alleviate the curse of dimensionality and greatly avoid model misspecification. We also derive some further properties of existing estimator with 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 propensity score, the bandwidth and kernel selections. The results show an essential difference from the IPW-based (unconditional) average treatment effect(ATE). The numerical studies indicate that for high-dimensional paradigms, the semiparametric-based estimator performs well in general {whereas nonparametric-based estimator, even sometimes, parametric-based estimator, is more affected by dimensionality. Some numerical studies are carried out to examine their performances. A real data example is analysed for illustration.