arXiv 31 Oct 2025 · Econometrics
arXiv:2511.00324 · PDF · DOI · OpenAlex · Extracted main text
We extend the approximate residual balancing (ARB) framework to nonlinear models, answering an open problem posed by Athey et al. (2018). Our approach addresses the challenge of estimating average treatment effects in high-dimensional settings where the outcome follows a generalized linear model. We derive a new bias decomposition for nonlinear models that reveals the need for a second-order correction to account for the curvature of the link function. Based on this insight, we construct balancing weights through an optimization problem that controls for both first and second-order sources of bias. We provide theoretical guarantees for our estimator, establishing its $\sqrt{n}$-consistency and asymptotic normality under standard high-dimensional 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 | Athey, Susan, Imbens, Guido, & Wager, Stefan (2018) Approximate residual balancing: debiased inference of average treatment effects in high dimensions | 0.928 | 4 | 3 | 100% |
| 2 | Javanmard, Adel, & Montanari, Andrea (2014) Confidence Intervals and Hypothesis Testing for High-Dimensional Regression | 0.644 | 2 | 2 | 100% |
| 3 | Robins, James, Li, Lingling, Tchetgen, Eric, & van der Vaart, Aad (2008) Higher order influence functions and minimax estimation of nonlinear functionals | 0.644 | 2 | 2 | 100% |
| 4 | Hirshberg, David A., & Wager, Stefan (2018) Debiased Inference of Average Partial Effects in Single-Index Models | 0.644 | 2 | 2 | 100% |
| 5 | Javanmard, Adel, & Montanari, Andrea (2018) Debiasing the lasso: Optimal sample size for Gaussian designs | 0.644 | 2 | 2 | 100% |
| 6 | Mackey, Lester, Syrgkanis, Vasilis, & Zadik, Ilias (2018) Orthogonal Machine Learning: Power and Limitations | 0.644 | 2 | 2 | 100% |
| 7 | Negahban, Sahand N., Ravikumar, Pradeep, Wainwright, Martin J., & Yu… (2012) A Unified Framework for High-Dimensional Analysis of $M$-Estimators with Decomposable Regularizers | 0.644 | 2 | 2 | 100% |
| 8 | Van de Geer, Sara A (2008) High-dimensional generalized linear models and the lasso | 0.644 | 2 | 2 | 100% |
| 9 | Bühlmann, Peter, & Van De Geer, Sara (2011) Statistics for high-dimensional data: Methods, theory and applications | 0.511 | 2 | 1 | 100% |
| 10 | Tsybakov, Alexandre B (2009) Introduction to Nonparametric Estimation | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 29 scored citations.