Non-Asymptotic Bounds of AIPW Estimators for Means with Missingness at Random

Abstract

The augmented inverse probability weighting is well known for its double robustness in missing data and causal inference. If either the propensity score model or the outcome regression model is correctly specified, the estimator is guaranteed to be consistent. Another important property of the augmented inverse probability weighting is that it can achieve first-order equivalence to the oracle estimator in which all nuisance parameters are known, even if the fitted models do not converge at the parametric root-n rate. We explore the non-asymptotic properties of the augmented inverse probability weighting estimator to infer the population mean with missingness at random. We also consider inferences of the mean outcomes on the observed group and on the unobserved group.