Tutorial: Deriving The Efficient Influence Curve for Large Models

Understand

This paper aims to provide a tutorial for upper level undergraduate and graduate students in statistics, biostatistics and epidemiology on deriving influence functions for non-parametric and semi-parametric models.

• The author will build on previously known efficiency theory and provide a useful identity and formulaic technique only relying on the basics of integration which, are self-contained in this tutorial and can be used in most any setting one might encounter in practice.
• The paper provides many examples of such derivations for well-known influence functions as well as for new parameters of interest.
• The influence function remains a central object for constructing efficient estimators for large models, such as the one-step estimator and the targeted maximum likelihood estimator.