AmirEmad Ghassami, James M. Robins, Andrea Rotnitzky
arXiv 27 May 2025 · Statistics — Methodology
arXiv:2505.20787 · PDF · DOI · OpenAlex · Extracted main text
In various statistical settings, the goal is to estimate a function which is restricted by the statistical model only through a conditional moment restriction. Prominent examples include the nonparametric instrumental variable framework for estimating the structural function of the outcome variable, and the proximal causal inference framework for estimating the bridge functions. A common strategy in the literature is to find the minimizer of the projected mean squared error. However, this approach can be sensitive to misspecification or slow convergence rate of the estimators of the involved nuisance components. In this work, we propose a debiased estimation strategy based on the influence function of a modification of the projected error and demonstrate its finite-sample convergence rate. Our proposed estimator possesses a second-order bias with respect to the involved nuisance functions and a desirable robustness property with respect to the misspecification of one of the nuisance functions. The proposed estimator involves a hyper-parameter, for which the optimal value depends on potentially unknown features of the underlying data-generating process. Hence, we further propose a hyper-parameter selection approach based on cross-validation and derive an error bound for the resulting estimator. This analysis highlights the potential rate loss due to hyper-parameter selection and underscore the importance and advantages of incorporating debiasing in this setting. We also study the application of our approach to the estimation of regular parameters in a specific parameter class, which are linear functionals of the solutions to the conditional moment restrictions and provide sufficient conditions for achieving root-n consistency using our debiased estimator.
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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 | Bennett, A., Kallus, N., Mao, X., Newey, W., Syrgkanis, V., and Ueha… (2023) Source condition double robust inference on functionals of inverse problems | 0.928 | 4 | 4 | 100% |
| 2 | van der Vaart, A. W., Dudoit, S., and van der Laan, M. J (2006) Oracle inequalities for multi-fold cross validation | 0.928 | 4 | 3 | 100% |
| 3 | Ghassami, A., Ying, A., Shpitser, I., and Tchetgen Tchetgen, E (2022) Minimax kernel machine learning for a class of doubly robust functionals with application to proximal causal inference self | 0.874 | 9 | 2 | 100% |
| 4 | Engl, H. W., Hanke, M., and Neubauer, A (1996) Regularization of inverse problems, volume 375 | 0.843 | 3 | 3 | 100% |
| 5 | Florens, J.-P., Johannes, J., and Van Bellegem, S (2011) Identification and estimation by penalization in nonparametric instrumental regression | 0.843 | 3 | 3 | 100% |
| 6 | van der Laan, M. J. and Dudoit, S (2003) Unified cross-validation methodology for selection among estimators and a general cross-validated adaptive epsilon-net estimator… | 0.843 | 3 | 3 | 100% |
| 7 | Cui, Y., Pu, H., Shi, X., Miao, W., and Tchetgen Tchetgen, E (2023) Semiparametric proximal causal inference | 0.811 | 4 | 2 | 100% |
| 8 | Foster, D. J. and Syrgkanis, V (2019) Orthogonal statistical learning | 0.737 | 3 | 2 | 100% |
| 9 | Kress, R (2013) Linear Integral Equations | 0.737 | 3 | 2 | 100% |
| 10 | Miao, W., Geng, Z., and Tchetgen Tchetgen, E. J (2018) Identifying causal effects with proxy variables of an unmeasured confounder | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 33 scored citations.