Robust propensity score weighting estimation under missing at random

Missing data is frequently encountered in many areas of statistics. One popular approach to address this issue is through the use of propensity score weighting. However, correctly specifying the statistical model can be a daunting task. Doubly robust estimation is attractive, as the consistency of the estimator is guaranteed when either the outcome regression model or the propensity score model is correctly specified. In this paper, we first employ information projection to develop an efficient and doubly robust estimator via indirect model calibration. The resulting propensity score estimator can be equivalently expressed as a doubly robust regression imputation estimator by imposing the internal bias calibration condition in estimating the regression parameters. In addition, using the gamma-divergence measure, we generalize the information projection to allow for outlier-robust propensity score estimation. The study includes the presentation of certain asymptotic properties and findings from a simulation study, which demonstrate that the proposed method enables robust inference, not only in cases of various model assumptions being violated but also in the presence of outliers. A real-life application is also presented using data from the Conservation Effects Assessment Project.