Kuanhao Jiang, Rajarshi Mukherjee, Subhabrata Sen, Pragya Sur
arXiv 20 May 2022 · Mathematics — Statistics Theory · publishedThe Annals of Statistics (2025) · 4 citations (OpenAlex)
arXiv:2205.10198 · PDF · DOI · OpenAlex · Extracted main text
Estimation of the average treatment effect (ATE) is a central problem in causal inference. In recent times, inference for the ATE in the presence of high-dimensional covariates has been extensively studied. Among the diverse approaches that have been proposed, augmented inverse probability weighting (AIPW) with cross-fitting has emerged a popular choice in practice. In this work, we study this cross-fit AIPW estimator under well-specified outcome regression and propensity score models in a high-dimensional regime where the number of features and samples are both large and comparable. Under assumptions on the covariate distribution, we establish a new central limit theorem for the suitably scaled cross-fit AIPW that applies without any sparsity assumptions on the underlying high-dimensional parameters. Our CLT uncovers two crucial phenomena among others: (i) the AIPW exhibits a substantial variance inflation that can be precisely quantified in terms of the signal-to-noise ratio and other problem parameters, (ii) the asymptotic covariance between the pre-cross-fit estimators is non-negligible even on the root-n scale. These findings are strikingly different from their classical counterparts. On the technical front, our work utilizes a novel interplay between three distinct tools--approximate message passing theory, the theory of deterministic equivalents, and the leave-one-out approach. We believe our proof techniques should be useful for analyzing other two-stage estimators in this high-dimensional regime. Finally, we complement our theoretical results with simulations that demonstrate both the finite sample efficacy of our CLT and its robustness to our assumptions.
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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 | barticle[author] Chernozhukov, VictorV., Chetverikov, DenisD., Demir… (2017) ) | 1.000 | 15 | 5 | 100% |
| 2 | barticle[author] Smucler, EzequielE., Rotnitzky, AndreaA. Robins, Ja… (2019) ) | 1.000 | 10 | 4 | 100% |
| 3 | barticle[author] Bang, HeejungH. Robins, James MJ. M (2005) ) | 1.000 | 8 | 3 | 100% |
| 4 | barticle[author] Sur, PragyaP. Candès, Emmanuel JE. J (2019) ) | 1.000 | 7 | 4 | 100% |
| 5 | barticle[author] Scharfstein, Daniel OD. O., Rotnitzky, AndreaA. Rob… (1999) ) | 0.874 | 6 | 2 | 100% |
| 6 | barticle[author] Tan, ZhiqiangZ (2020) ) | 0.874 | 5 | 2 | 100% |
| 7 | barticle[author] Donoho, David LD. L., Maleki, ArianA. Montanari, An… (2009) ) | 0.843 | 3 | 3 | 100% |
| 8 | barticle[author] Bean, DerekD., Bickel, Peter JP. J., El Karoui, Nou… (2013) ) | 0.811 | 4 | 2 | 100% |
| 9 | barticle[author] El Karoui, NoureddineN., Bean, DerekD., Bickel, Pet… (2013) ) | 0.811 | 4 | 2 | 100% |
| 10 | barticle[author] El Karoui, NoureddineN (2018) ) | 0.811 | 4 | 2 | 100% |
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