Inverse probability tilting and missing data problems2008

"This paper outlines a new minimum empirical discrepancy (MD) estimator for missing data, sample combination and related problems: inverse probability tilting (IPT). Covered examples include estimation of the average treatment effect (ATE), the average treatment effect on the treated (ATT) and the two sample instrumental variables (TSIV) model. The proposed estimator attains the semiparametric efficiency bound under two auxiliary parametric restrictions (local efficiency), but is consistent so long as one or the other holds (double robustness). A novel feature of IPT is its 'exact balancing' property: after reweighting, sample moments of always-observed covariates in the complete-case subsample equal their corresponding (unweighted) full sample means. We also show how prior...