cross-fitting

Introduction Two powerful tools in causal inference are the Augmented Inverse Propensity Weighting (AIPW) estimator and the Residual-on-Residual regression estimator for partially linear models. Drawing from Wager’s notes (2024), this post breaks down how these estimators work, compares their strengths and weaknesses, and offers tips for when to use each.

Debiased machine learning (DML) is a generic recipe. The idea behind it is adding a correction term to the plug-in estimator of the functional, which leads to properties such as semi-parametric efficiency, double robustness, and Neyman orthogonality.

Motivation & Intuition In classical semiparametric theory, we want to estimate a low‑dimensional target parameter (say, a treatment effect) while controlling for high‑dimensional nuisance functions (like nonparametric regressions). However, in order to use the central limit theorem (CLT) and to characterize the asymptotic behavior, classical results require that the space of functions in which these nuisance functions lie is “small” in a technical sense.