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Abstract:
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Estimation of treatment effects with a large number of covariates has received considerable attention in recent years. Most of the existing methods require specifying certain parametric models involving the outcome, treatment and confounding variables, and employ a variable selection procedure to identify confounders. However, selection of the right set of confounders depends on correct specification of the working models. The bias due to model misspecification and incorrect selection of confounders can yield misleading results. We proposes a new robust and efficient approach for inference about the average treatment effect via a flexible modeling strategy incorporating penalized variable selection. Specifically, we consider an estimator constructed based on an efficient influence function which involves a propensity score function and an outcome regression function. We then propose a new sparse sufficient dimension reduction approach to estimating these two functions, without making restrictive parametric modeling assumptions. We show that the proposed estimator of the average treatment effect is asymptotically normal and semiparametric efficient.
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