Imputation is all you need: double robustness, semiparametric efficiency, and automatic covariate balance for estimating the average treatment effect
Abstract
Imputation-based causal estimation is typically viewed as relying exclusively on an outcome model, in contrast to augmented inverse-probability weighting, whose consistency is protected by fitting two nuisance models. This paper argues that this view can be misleading by highlighting a hidden dual weighting structure in least-squares sieve regression imputation. Although only outcome regressions are explicitly fitted, the resulting imputation estimator admits an exact weighting representation whose induced weights balance every function in the sieve space and the corresponding population weighting functions are the L2 projections of the inverse propensity scores onto the same sieve space. This projection structure yields an implicit form of double robustness and, under standard sieve approximation and growth conditions, asymptotic linearity with the efficient influence function. Thus, weighting, covariate balance, double robustness, and semiparametric efficiency can all emerge from imputation alone through the geometry of least-squares projection.
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BibTeX
@misc{han2026imputation,
title = {{Imputation is all you need: double robustness, semiparametric efficiency, and automatic covariate balance for estimating the average treatment effect}},
author = {Fang Han and Peng Ding},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38692},
eprint = {2609.38692},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38692},
}
RIS
TY - UNPB
TI - Imputation is all you need: double robustness, semiparametric efficiency, and automatic covariate balance for estimating the average treatment effect
AU - Fang Han
AU - Peng Ding
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.38692
UR - https://arxiv.org/abs/2609.38692
AB - Imputation-based causal estimation is typically viewed as relying exclusively on an outcome model, in contrast to augmented inverse-probability weighting, whose consistency is protected by fitting two nuisance models. This paper argues that this view can be misleading by highlighting a hidden dual weighting structure in least-squares sieve regression imputation. Although only outcome regressions are explicitly fitted, the resulting imputation estimator admits an exact weighting representation whose induced weights balance every function in the sieve space and the corresponding population weighting functions are the L^2 projections of the inverse propensity scores onto the same sieve space. This projection structure yields an implicit form of double robustness and, under standard sieve approximation and growth conditions, asymptotic linearity with the efficient influence function. Thus, weighting, covariate balance, double robustness, and semiparametric efficiency can all emerge from imputation alone through the geometry of least-squares projection.
ER -