Semiparametric doubly robust targeted double machine learning: a review

TL;DR

This review discusses efficient nonparametric estimation methods for causal inference, emphasizing theoretical bounds, estimator analysis, and practical approaches to achieve optimal performance.

Contribution

It provides a comprehensive overview of efficiency bounds and estimator analysis in semiparametric causal inference, with practical insights and simplified explanations.

Findings

Efficiency bounds for causal parameters are characterized.

Estimators can attain these bounds under weak assumptions.

Practical shortcuts facilitate derivations and understanding.

Abstract

In this review we cover the basics of efficient nonparametric parameter estimation (also called functional estimation), with a focus on parameters that arise in causal inference problems. We review both efficiency bounds (i.e., what is the best possible performance for estimating a given parameter?) and the analysis of particular estimators (i.e., what is this estimator's error, and does it attain the efficiency bound?) under weak assumptions. We emphasize minimax-style efficiency bounds, worked examples, and practical shortcuts for easing derivations. We gloss over most technical details, in the interest of highlighting important concepts and providing intuition for main ideas.