Bounded, Efficient, and Doubly Robust Estimation with Inverse Weighting

Consider the problem of estimating the mean of an outcome in the presence of missing data or estimating population average treatment effects in causal inference. A doubly robust estimator remains consistent if an outcome regression model or a propensity score model is correctly specified. We build on the nonparametric likelihood approach of Tan and propose new doubly robust estimators. These estimators have desirable properties in efficiency if the propensity score model is correctly specified, and in boundedness even if the inverse probability weights are highly variable. We compare new and existing estimators in a simulation study and find that the robustified likelihood estimators yield overall the smallest mean squared errors.