Fang Han, Peng Ding
arXiv 30 Sep 2026 · Mathematics — Statistics Theory
arXiv:2609.38692 · PDF · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Imbens, Guido W and Newey, Whitney K and Ridder, Geert (2005) Mean-square-error calculations for average treatment effects | 1.000 | 10 | 4 | 100% |
| 2 | Lin, Zhexiao and Han, Fang (2025) On regression-adjusted imputation estimators of the average treatment effect self | 1.000 | 7 | 3 | 100% |
| 3 | Hahn, Jinyong (1998) On the role of the propensity score in efficient semiparametric estimation of average treatment effects | 0.928 | 4 | 3 | 100% |
| 4 | Lin, Zhexiao and Ding, Peng and Han, Fang (2023) Estimation based on nearest neighbor matching: from density ratio to average treatment effect self | 0.928 | 4 | 3 | 100% |
| 5 | Wang, Ruoyu and Su, Miaomiao and Wang, Qihua (2023) Distributed nonparametric regression imputation for missing response problems with large-scale data | 0.874 | 10 | 2 | 100% |
| 6 | Chan, Kwun Chuen Gary and Yam, Sheung Chi Phillip and Zhang, Zheng (2016) Globally efficient non-parametric inference of average treatment effects by empirical balancing calibration weighting | 0.874 | 5 | 2 | 100% |
| 7 | Abadie, A. and Imbens, G. W (2011) Bias-corrected matching estimators for average treatment effects | 0.811 | 4 | 2 | 100% |
| 8 | Chattopadhyay, Ambarish and Zubizarreta, Jose R (2023) On the implied weights of linear regression for causal inference | 0.811 | 4 | 2 | 100% |
| 9 | Robins, James and Sued, Mariela and Lei-Gomez, Quanhong and Rotnitzk… (2007) Comment: Performance of double-robust estimators when “inverse probability” weights are highly variable | 0.811 | 4 | 2 | 100% |
| 10 | Belloni, Alexandre and Chernozhukov, Victor and Chetverikov, Denis a… (2015) Some new asymptotic theory for least squares series: pointwise and uniform results | 0.737 | 3 | 2 | 100% |
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