asymptotic-theory

What problem does it solve?

This skill provides rigorous theoretical tools for statistical inference in semi-parametric models, enabling precise efficiency analysis and robust estimation.

Core Features & Use Cases

• Semiparametric efficiency bounds and influence function theory for causal estimands (ATE, NIE, NDE).
• M-estimation framework and asymptotic normality with sandwich variance calculations.
• Double robustness and efficient estimation strategies (TMLE, one-step estimators) for robust causal inference in observational data.
• Guidance for variance estimation, bootstrap, and inference under model misspecification.

Quick Start

• Define the estimand and nuisance models (e.g., propensity score, outcome regression).
• Derive the efficient influence function and implement an estimator (e.g., TMLE or one-step) using your data.
• Validate assumptions and compute variance with the sandwich estimator or bootstrapping.