Asymptotic Theory

Rigorous framework for statistical inference and efficiency in modern methodology

Use this skill when working on: asymptotic properties of estimators, influence functions, semiparametric efficiency, double robustness, variance estimation, confidence intervals, hypothesis testing, M-estimation, or deriving limiting distributions.

Efficiency Bounds

Semiparametric Efficiency Theory

Cramér-Rao Lower Bound: For any unbiased estimator, $$\text{Var}(\hat{\theta}) \geq \frac{1}{nI(\theta)}$$

where $I(\theta)$ is the Fisher information.

Semiparametric Efficiency Bound: The variance of the efficient influence function: $$V_{eff} = E[\phi^*(\theta_0)^2]$$