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

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