Chunrong Ai, Jiawei Shan
arXiv 4 Jan 2025 · Statistics — Methodology · publishedStatistica Sinica (2025)
arXiv:2501.02214 · PDF · DOI · OpenAlex · Extracted main text
One approach to estimating the average treatment effect in binary treatment with unmeasured confounding is the proximal causal inference, which assumes the availability of outcome and treatment confounding proxies. The key identifying result relies on the existence of a so-called bridge function. A parametric specification of the bridge function is usually postulated and estimated using standard techniques. The estimated bridge function is then plugged in to estimate the average treatment effect. This approach may have two efficiency losses. First, the bridge function may not be efficiently estimated since it solves an integral equation. Second, the sequential procedure may fail to account for the correlation between the two steps. This paper proposes to approximate the integral equation with increasing moment restrictions and jointly estimate the bridge function and the average treatment effect. Under sufficient conditions, we show that the proposed estimator is efficient. To assist implementation, we propose a data-driven procedure for selecting the tuning parameter (i.e., number of moment restrictions). Simulation studies reveal that the proposed method performs well in finite samples, and application to the right heart catheterization dataset from the SUPPORT study demonstrates its practical value.
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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 | Cui, Pu, Shi, Miao \ Tchetgen Tchetgen (2023) `Semiparametric proximal causal inference', Journal of the American Statistical Association 0(0), 1–12 | 1.000 | 11 | 5 | 100% |
| 2 | Tchetgen Tchetgen, Ying, Cui, Shi \ Miao (2024) `An introduction to proximal causal inference', Statistical Science in press | 1.000 | 10 | 3 | 100% |
| 3 | Miao, Shi, Li \ Tchetgen Tchetgen (2024) `A confounding bridge approach for double negative control inference on causal effects', Statistical Theory and Related Fields 8… | 0.928 | 4 | 3 | 100% |
| 4 | Donald, Imbens \ Newey (2009) `Choosing instrumental variables in conditional moment restriction models', Journal of Econometrics 152(1), 28–36 | 0.843 | 4 | 3 | 75% |
| 5 | Ai \ Chen (2012) `The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions', Journal of Econ… | 0.737 | 5 | 3 | 40% |
| 6 | Brown \ Newey (1998) `Efficient semiparametric estimation of expectations', Econometrica 66(2), 453–464 | 0.737 | 3 | 3 | 67% |
| 7 | Hansen (1982) `Large sample properties of generalized method of moments estimators', Econometrica 50(4), 1029–1054 | 0.737 | 3 | 2 | 100% |
| 8 | Miao, Geng \ Tchetgen Tchetgen (2018) `Identifying causal effects with proxy variables of an unmeasured confounder', Biometrika 105(4), 987–993 | 0.737 | 3 | 2 | 100% |
| 9 | Chen (2007) Large sample sieve estimation of semi-nonparametric models, in J. J | 0.644 | 2 | 2 | 100% |
| 10 | Newey (1997) `Convergence rates and asymptotic normality for series estimators', Journal of Econometrics 79(1), 147–168 | 0.644 | 2 | 2 | 100% |
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