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Course: Finite Sample and Asymptotic Estimators in Causal Inference

A self-contained course covering the theoretical and methodological foundations of causal inference estimators — from potential outcomes to doubly-robust methods — with finite-sample and asymptotic analyses.

1. Chapter 1 — Statistical Introduction — Definitions of statistical models, estimators, and asymptotic theory — the mathematical foundations for causal inference.
2. Chapter 2 — Potential Outcomes — The Neyman-Rubin potential outcomes framework and the fundamental problem of causal inference.
3. Chapter 3 — Randomized Controlled Trials — Key assumptions and setup for randomized controlled trials: no interference, SUTVA, and randomization.
4. Chapter 4 — RCT Estimators — Horvitz-Thomson, Hajek, regression-based and doubly-robust estimators for the ATE in RCTs, with finite-sample and asymptotic analyses.
5. Chapter 5 — Observational Trials — How observational studies differ from RCTs and the challenges of confounding in real-world data.
6. Chapter 6 — Inverse Propensity Weighting — Oracle and estimated IPW estimators, their asymptotic properties, and the role of propensity score estimation.
7. Chapter 7 — Augmented Inverse Propensity Weighting — The doubly-robust AIPW estimator: combining outcome modelling and propensity weighting with semiparametric efficiency.