semiparametric efficiency

Causal inference promises to answer “what if” questions from observational data. But the standard approach — specify a parametric model, fit it, report the estimate — breaks down under misspecification. And misspecification is the norm, not the exception.

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.

The following exercise is from CausalAIBook Notebook. The goal is to illustrate the difference between Neyman orthogonal vs non-orthogonal approach. Setting We compare the performance of the naive and orthogonal methods in a computational experiment where \(p=n=100\), \(\beta_j = 1/j^2\), \((\gamma_{DW})_j = 1/j^2\) and \[Y = 1 \cdot D + \beta' W + \epsilon_Y\]

Motivation Semiparametric models contain both a finite-dimensional parameter of interest ($\theta$) and an infinite-dimensional nuisance parameter ($\eta$). The goal is to estimate $\theta$ as efficiently as possible while filtering out the impact of $\eta$.

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.