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When estimating the treatment effect in an observational study, we use asemiparametric locally efficient dimension reduction approach to assess boththe treatment assignment mechanism and the average responses in both treatedand nontreated groups. We then integrate all results through imputation,inverse probability weighting and doubly robust augmentation estimators. Doublyrobust estimators are locally efficient while imputation estimators aresuper-efficient when the response models are correct. To take advantage of bothprocedures, we introduce a shrinkage estimator to automatically combine thetwo, which retains the double robustness property while improving on thevariance when the response model is correct. We demonstrate the performance ofthese estimators through simulated experiments and a real dataset concerningthe effect of maternal smoking on baby birth weight.  Key words and phrases: Average Treatment Effect, Doubly Robust Estimator,Efficiency, Inverse Probability Weighting, Shrinkage Estimator.

Sufficient Dimension Reduction for Feasible and Robust Estimation of Average Causal Effect