Imputation is all you need: double robustness, semiparametric efficiency, and automatic covariate balance for estimating the average treatment effect

2026-09-29

AI Summary

This study addresses the prevailing perception that conventional imputation methods lack double robustness and statistical efficiency. By leveraging least squares sieve regression, inverse propensity score L2 projection, and asymptotic linear analysis, this work uncovers a latent dual-weighting structure inherent in such imputation procedures. We demonstrate that imputation alone can achieve automatic covariate balancing and implicit double robustness without separately fitting outcome and propensity score models, thereby challenging established assumptions. Furthermore, we show that the imputation estimator admits an exact weighting representation and attains optimal efficiency by reaching the semiparametric efficient influence function bound. Collectively, these findings establish a novel paradigm for causal inference that integrates theoretical completeness with computational simplicity.

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 $L^2$ 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.

Problem

• causal inference
• imputation
• double robustness
• average treatment effect
• semiparametric efficiency

Innovation

• imputation
• double robustness
• semiparametric efficiency
• sieve regression
• covariate balance