Semiparametric theory

TL;DR

This paper reviews semiparametric theory, emphasizing influence functions, and discusses how it enables robust estimation of causal effects with partially unspecified models.

Contribution

It provides a concise overview of semiparametric theory and highlights the role of influence functions in robust causal inference.

Findings

Semiparametric models allow flexible data-generating processes.

Influence functions are central to deriving robust estimators.

Semiparametric estimators can achieve fast convergence rates.

Abstract

In this paper we give a brief review of semiparametric theory, using as a running example the common problem of estimating an average causal effect. Semiparametric models allow at least part of the data-generating process to be unspecified and unrestricted, and can often yield robust estimators that nonetheless behave similarly to those based on parametric likelihood assumptions, e.g., fast rates of convergence to normal limiting distributions. We discuss the basics of semiparametric theory, focusing on influence functions.