# Causal inference with a functional outcome

arXiv: https://arxiv.org/abs/2304.07113 · HTML: https://mlsanity.com/paper/2304.07113/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2023.

## Built on by (most cited first, 8 of 8)

- [Kernel-based estimators for functional causal effects](https://mlsanity.com/paper/2503.05024/) (2025)
- [Topological Causal Effects](https://mlsanity.com/paper/2603.02289/) (2026)
- [The Causal Impact of Credit Lines on Spending Distributions](https://mlsanity.com/paper/2312.10388/) (2023)
- [A Doubly Robust Machine Learning Approach for Disentangling Treatment Effect Heterogeneity with Functional Outcomes](https://mlsanity.com/paper/2602.11118/) (2026)
- [Beyond Means: Topological Causal Effects under Persistent-Homology Ignorability](https://mlsanity.com/paper/2603.14169/) (2026)
- [Topological Ignorability for Structural Causal Effects Beyond Means](https://mlsanity.com/paper/2606.01184/) (2026)
- [Wasserstein Policy Learning for Distributional Outcomes](https://mlsanity.com/paper/2606.19117/) (2026)
- [Functional Causal Discovery via Conditional Covariance Ordering](https://mlsanity.com/paper/2609.27256/) (2026)

## Abstract (arXiv)

This paper presents methods to study the causal effect of a binary treatment on a functional outcome with observational data. We define a Functional Average Treatment Effect and develop an outcome regression estimator. We show how to obtain valid inference on the FATE using simultaneous confidence bands, which cover the FATE with a given probability over the entire domain. Simulation experiments illustrate how the simultaneous confidence bands take the multiple comparison problem into account. Finally, we use the methods to infer the effect of early adult location on subsequent income development for one Swedish birth cohort.