The Influence Function of Semiparametric Estimators

Understand

Many useful parameters depend on nonparametric first steps.

• Examples include games, dynamic discrete choice, average exact consumer surplus, and treatment effects.
• Often estimators of these parameters are asymptotically equivalent to a sample average of an object referred to as the influence function.
• The influence function is useful in local policy analysis, in evaluating local sensitivity of estimators, constructing debiased machine learning estimators, in efficiency comparisons, and in formulating primitive regularity conditions for asymptotic normality, We show that the influence function is a Gateaux derivative with respect to a smooth deviation evaluated at a point mass.