AmirEmad Ghassami, Andrew Ying, Ilya Shpitser, Eric Tchetgen Tchetgen
arXiv 7 Apr 2021 · Statistics — Machine Learning · 9 citations (OpenAlex)
arXiv:2104.02929 · PDF · DOI · OpenAlex · Extracted main text
Robins et al. (2008) introduced a class of influence functions (IFs) which could be used to obtain doubly robust moment functions for the corresponding parameters. However, that class does not include the IF of parameters for which the nuisance functions are solutions to integral equations. Such parameters are particularly important in the field of causal inference, specifically in the recently proposed proximal causal inference framework of Tchetgen Tchetgen et al. (2020), which allows for estimating the causal effect in the presence of latent confounders. In this paper, we first extend the class of Robins et al. to include doubly robust IFs in which the nuisance functions are solutions to integral equations. Then we demonstrate that the double robustness property of these IFs can be leveraged to construct estimating equations for the nuisance functions, which enables us to solve the integral equations without resorting to parametric models. We frame the estimation of the nuisance functions as a minimax optimization problem. We provide convergence rates for the nuisance functions and conditions required for asymptotic linearity of the estimator of the parameter of interest. The experiment results demonstrate that our proposed methodology leads to robust and high-performance estimators for average causal effect in the proximal causal inference framework.
appendix boundary found by appendix_command · 46% of the source is main text. Read the extracted text to check this.
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 | Robins, J., Li, L., Tchetgen Tchetgen, E., van der Vaart, A., et al (2008) Higher order influence functions and minimax estimation of nonlinear functionals | 0.956 | 8 | 4 | 88% |
| 2 | Tchetgen Tchetgen, E. J., Ying, A., Cui, Y., Shi, X., and Miao, W (2020) An introduction to proximal causal learning self | 0.894 | 7 | 5 | 71% |
| 3 | Cui, Y., Pu, H., Shi, X., Miao, W., and Tchetgen Tchetgen, E (2020) Semiparametric proximal causal inference | 0.863 | 14 | 5 | 64% |
| 4 | Miao, W., Geng, Z., and Tchetgen Tchetgen, E. J (2018) Identifying causal effects with proxy variables of an unmeasured confounder | 0.830 | 7 | 3 | 57% |
| 5 | Dikkala, N., Lewis, G., Mackey, L., and Syrgkanis, V (2020) Minimax estimation of conditional moment models | 0.754 | 14 | 4 | 43% |
| 6 | Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C… (2018) Double/debiased machine learning for treatment and structural parameters | 0.693 | 9 | 3 | 33% |
| 7 | Hernán, M. A. and Robins, J. M (2020) Causal inference: what if | 0.644 | 2 | 2 | 100% |
| 8 | Van der Vaart, A. W (2000) Asymptotic statistics, volume 3 | 0.644 | 2 | 2 | 100% |
| 9 | Chen, X. and Pouzo, D (2012) Estimation of nonparametric conditional moment models with possibly nonsmooth generalized residuals | 0.585 | 4 | 3 | 25% |
| 10 | Kallus, N., Mao, X., and Uehara, M (2021) Causal inference under unmeasured confounding with negative controls: A minimax learning approach | 0.575 | 7 | 1 | 57% |
Showing the top 10 of 74 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.