Three-way Cross-Fitting and Pseudo-Outcome Regression for Estimation of Conditional Effects and other Linear Functionals

TL;DR

This paper introduces a novel method combining 3-way cross-fitting and pseudo-outcome regression to improve the estimation of individual treatment effects, achieving faster convergence rates with flexible machine learning models.

Contribution

It develops a new approach that integrates 3-way cross-fitting with pseudo-outcome regression for personalized effect estimation, enhancing efficiency and convergence.

Findings

Achieves faster convergence rates under smoothness conditions.

Combines multiple advanced estimation techniques for improved accuracy.

Provides theoretical guarantees for the proposed method.

Abstract

We propose an approach to better inform treatment decisions at an individual level by adapting recent advances in average treatment effect estimation to conditional average treatment effect estimation. Our work is based on doubly robust estimation methods, which combine flexible machine learning tools to produce efficient effect estimates while relaxing parametric assumptions about the data generating process. Refinements to doubly robust methods have achieved faster convergence by incorporating 3-way cross-fitting, which entails dividing the sample into three partitions, using the first to estimate the conditional probability of treatment, the second to estimate the conditional expectation of the outcome, and the third to perform a first order bias correction step. Here, we combine the approaches of 3-way cross-fitting and pseudo-outcome regression to produce personalized effect estimates. We show that this approach yields fast convergence rates under a smoothness condition on the conditional expectation of the outcome.