Estimation with missing data: beyond double robustness

We propose an estimator that is more robust than doubly robust estimators, based on weighting complete cases using weights other than inverse probability when estimating the population mean of a response variable subject to ignorable missingness. We allow multiple models for both the propensity score and the outcome regression. Our estimator is consistent if any of the multiple models is correctly specified. Such multiple robustness against model misspecification is a significant improvement over double robustness, which allows only one propensity score model and one outcome regression model. Our estimator attains the semiparametric efficiency bound when one propensity score model and one outcome regression model are correctly specified, without requiring knowledge of which models are correct.