Jianxuan Liu

The problem of estimating average treatment effectis of fundamental importance when evaluating the effectiveness ofmedical treatments or social intervention policies. Most of the ex-isting methods for estimating average treatment effect rely on someparametric assumptions onthe propensity score model or outcomeregression model one way or the other. In reality, both models areprone to misspecification, which can have undue influence on the es-timated averagetreatment effect. We propose a new robust approachto estimating the average treatment effect based on observationaldata in the challenging situation when neither a plausible paramet-ricoutcome model nor a reliable parametric propensity score model isavailable. Our estimator can be considered as a robust extension ofthe popular class of propensity score weighted estimators. The newapproach has the advantage of being robust, flexible, data adap-tive and it can handle many covariates simultaneously. Adaptinga dimension reduction approach, we estimate the propensity scoreweights semiparametrically by using a nonparametric link functionto relate the treatment assignment indicator to a low-dimensionalstructure of the covariates which are formed typically by severallinear combinations of the covariates. We develop a class of consis-tent estimators for the average treatment effect and studied theirtheoretical properties. We demonstrate the robust performance ofthe new estimators on simulated data and a real dataexample ofanalyzing the effect of maternal smoking on babies’ birth weight.