Structure-agnostic Optimality of Doubly Robust Learning for Treatment Effect Estimation

TL;DR

This paper proves the statistical optimality of doubly robust estimators for treatment effect estimation within a structure-agnostic framework, highlighting their effectiveness even without parametric assumptions.

Contribution

It establishes the optimality of doubly robust estimators for ATE and ATT under a flexible, structure-agnostic framework using black-box estimation procedures.

Findings

Doubly robust estimators are statistically optimal in a broad, structure-agnostic setting.

The results apply to both ATE and ATT, including weighted variants for policy evaluation.

The framework does not require parametric assumptions on nuisance functions.

Abstract

Average treatment effect estimation is the most central problem in causal inference with application to numerous disciplines. While many estimation strategies have been proposed in the literature, the statistical optimality of these methods has still remained an open area of investigation, especially in regimes where these methods do not achieve parametric rates. In this paper, we adopt the recently introduced structure-agnostic framework of statistical lower bounds, which poses no structural properties on the nuisance functions other than access to black-box estimators that achieve some statistical estimation rate. This framework is particularly appealing when one is only willing to consider estimation strategies that use non-parametric regression and classification oracles as black-box sub-processes. Within this framework, we prove the statistical optimality of the celebrated and widely used doubly robust estimators for both the Average Treatment Effect (ATE) and the Average Treatment Effect on the Treated (ATT), as well as weighted variants of the former, which arise in policy evaluation.