Augmented balancing weights as linear regression

• 成果类型: Article; Early Access
• 署名作者: Bruns-Smith, David; Dukes, Oliver; Feller, Avi; Ogburn, Elizabeth L.
• 署名单位: Stanford University; Ghent University; University of California System; University of California Berkeley; Johns Hopkins University; Johns Hopkins Bloomberg School of Public Health
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkaf019
• 发表日期: 2025
• 关键词: calibration estimators; inference; causal

摘要

We provide a novel characterization of augmented balancing weights, also known as automatic debiased machine learning. These popular doubly robust estimators combine outcome modelling with balancing weights-weights that achieve covariate balance directly instead of estimating and inverting the propensity score. When the outcome and weighting models are both linear in some (possibly infinite) basis, we show that the augmented estimator is equivalent to a single linear model with coefficients that combine those of the original outcome model with those from unpenalized ordinary least-squares (OLS). Under certain choices of regularization parameters, the augmented estimator in fact collapses to the OLS estimator alone. We then extend these results to specific outcome and weighting models. We first show that the augmented estimator that uses (kernel) ridge regression for both outcome and weighting models is equivalent to a single, undersmoothed (kernel) ridge regression-implying a novel analysis of undersmoothing. When the weighting model is instead lasso-penalized, we demonstrate a familiar 'double selection' property. Our framework opens the black box on this increasingly popular class of estimators, bridges the gap between existing results on the semiparametric efficiency of undersmoothed and doubly robust estimators, and provides new insights into the performance of augmented balancing weights.