Semiparametric Efficiency Theory as Differential Calculus on a Space of Probability Distributions (opens in new tab)

Semiparametric efficiency theory provides the mathematical foundation for influence-function-based estimation, including one-step estimators, targeted minimum loss estimators, and many modern inferential methods used in causal inference and missing data analysis. Despite its widespread use, the theory is often presented through a collection of technical constructions whose geometric meaning remains opaque. As a result, influence functions are of...