Residual Balancing for Non-Linear Outcome Models in High Dimensions

TL;DR

This paper extends the approximate residual balancing framework to nonlinear outcome models in high-dimensional settings, introducing a second-order correction for bias and providing theoretical guarantees for the estimator.

Contribution

It develops a novel bias correction method for nonlinear models in high dimensions, addressing an open problem and ensuring $\

Findings

Achieves $\

paper_type":"method"}}Let's analyze the paper and extract the structured metadata accordingly. The paper extends the approximate residual balancing (ARB) framework to nonlinear models, specifically addressing high-dimensional generalized linear models. It introduces a second-order bias correction and constructs balancing weights through an optimization problem, with theoretical guarantees such as $\\sqrt{n}$-consistency and asymptotic normality. The key novelty is the extension of ARB to nonlinear outcomes with a bias correction that accounts for the curvature of the link function. The concrete results include establishing the estimator's statistical properties under standard assumptions. The paper type is a method paper, as it proposes a new estimation technique with theoretical analysis. Based on this, the JSON output is: ```json {

contribution":"It develops a novel bias correction method for nonlinear models in high dimensions, addressing an open problem and ensuring $\

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.