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Residual Balancing for Non-Linear Outcome Models in High Dimensions

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  • Isaac Meza

Abstract

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.

Suggested Citation

  • Isaac Meza, 2025. "Residual Balancing for Non-Linear Outcome Models in High Dimensions," Papers 2511.00324, arXiv.org.
    • Handle: RePEc:arx:papers:2511.00324
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    References listed on IDEAS

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    1. Kosuke Imai & Marc Ratkovic, 2014. "Covariate balancing propensity score," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 243-263, January.
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    3. Kwun Chuen Gary Chan & Sheung Chi Phillip Yam & Zheng Zhang, 2016. "Globally efficient non-parametric inference of average treatment effects by empirical balancing calibration weighting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 673-700, June.
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    7. Susan Athey & Guido W. Imbens & Stefan Wager, 2018. "Approximate residual balancing: debiased inference of average treatment effects in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 597-623, September.
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