Semiparametric theory and empirical processes in causal inference

TL;DR

This paper reviews semiparametric theory and empirical process tools essential for causal inference, emphasizing their role in handling complex models and integrating modern machine learning methods.

Contribution

It provides a comprehensive overview of semiparametric models and empirical process theory in causal inference, highlighting their applications and future research directions.

Findings

Semiparametric models effectively handle complex causal data.

Empirical process theory aids in understanding estimator asymptotics.

Framework supports integration of machine learning in causal analysis.

Abstract

In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss estimation and inference for causal effects under semiparametric models, which allow parts of the data-generating process to be unrestricted if they are not of particular interest (i.e., nuisance functions). These models are very useful in causal problems because the outcome process is often complex and difficult to model, and there may only be information available about the treatment process (at best). Semiparametric theory gives a framework for benchmarking efficiency and constructing estimators in such settings. In the second part of the paper we discuss empirical process theory, which provides powerful tools for understanding the asymptotic behavior of semiparametric estimators that depend on flexible nonparametric estimators of nuisance functions. These tools are crucial for incorporating machine learning and other modern methods into causal inference analyses. We conclude by examining related extensions and future directions for work in semiparametric causal inference.