  Imputing missing potential outcomes using an estimated regression function is
a natural idea for estimating causal effects. In the literature, estimators
that combine imputation and regression adjustments are believed to be
comparable to augmented inverse probability weighting. Accordingly, people for
a long time conjectured that such estimators, while avoiding directly
constructing the weights, are also doubly robust (Imbens, 2004; Stuart, 2010).
Generalizing an earlier result of the authors (Lin et al., 2021), this paper
formalizes this conjecture, showing that a large class of regression-adjusted
imputation methods are indeed doubly robust for estimating the average
treatment effect. In addition, they are provably semiparametrically efficient
as long as both the density and regression models are correctly specified.
Notable examples of imputation methods covered by our theory include kernel
matching, (weighted) nearest neighbor matching, local linear matching, and
(honest) random forests.
