TY - JOUR
T1 - On IPW-based estimation of conditional average treatment effects
AU - Zhou, Niwen
AU - ZHU, Lixing
N1 - Funding Information:
The authors? s research was supported by a grant from the University Grants Council of Hong Kong. The authors thank the editor, associate editor and referees for their constructive comments and suggestions that led to an improvement of an early manuscript.
PY - 2021/12
Y1 - 2021/12
N2 - 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.
AB - 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.
KW - Dimension reduction
KW - Heterogeneity treatment effects
KW - Propensity score
UR - http://www.scopus.com/inward/record.url?scp=85102317564&partnerID=8YFLogxK
U2 - 10.1016/j.jspi.2021.02.003
DO - 10.1016/j.jspi.2021.02.003
M3 - Journal article
AN - SCOPUS:85102317564
SN - 0378-3758
VL - 215
SP - 1
EP - 22
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
ER -