Doubly-Robust Functional Average Treatment Effect Estimation

TL;DR

This paper introduces DR-FoS, a new method for estimating causal effects on functional data that remains reliable even if some models are misspecified, with proven theoretical properties and practical validation.

Contribution

We develop DR-FoS, a double robust estimator for the Functional Average Treatment Effect, combining functional data analysis with causal inference for the first time.

Findings

DR-FoS provides consistent FATE estimates under model misspecification.

The estimator's asymptotic distribution is Gaussian, enabling valid inference.

Simulation results demonstrate robustness across various scenarios.

Abstract

Understanding causal relationships in the presence of complex, structured data remains a central challenge in modern statistics and science in general. While traditional causal inference methods are well-suited for scalar outcomes, many scientific applications demand tools capable of handling functional data -- outcomes observed as functions over continuous domains such as time or space. Motivated by this need, we propose DR-FoS, a novel method for estimating the Functional Average Treatment Effect (FATE) in observational studies with functional outcomes. DR-FoS exhibits double robustness properties, ensuring consistent estimation of FATE even if either the outcome or the treatment assignment model is misspecified. By leveraging recent advances in functional data analysis and causal inference, we establish the asymptotic properties of the estimator, proving its convergence to a Gaussian process. This guarantees valid inference with simultaneous confidence bands across the entire functional domain. Through extensive simulations, we show that DR-FoS achieves robust performance under a wide range of model specifications. Finally, we illustrate the utility of DR-FoS in a real-world application, analyzing functional outcomes to uncover meaningful causal insights in the SHARE ({\em Survey of Health, Aging and Retirement in Europe}) dataset.