Title: Doubly robust estimation of causal effects for random object outcomes with continuous treatments
Authors: Satarupa Bhattacharjee, Bing Li, Xiao Wu, Lingzhou Xue
Abstract: Causal inference is central to statistics and scientific discovery, enabling researchers to identify cause-and-effect relationships beyond associations. Although traditionally studied within Euclidean spaces, contemporary applications increasingly involve complex, non-Euclidean data structures that reside in abstract metric spaces known as random objects, such as images, shapes, networks, and distributions.
This paper introduces a novel framework for causal inference with continuous treatments applied to non-Euclidean data. To address the challenges posed by the lack of linear structures, we leverage Hilbert space embeddings of the metric spaces to facilitate Frechet mean estimation and causal effect mapping. Motivated by a study on the impact of exposure to fine particulate matter on age-at-death distributions across U.S. counties, we propose a nonparametric, doubly-debiased causal inference approach for outcomes as random objects with continuous treatments.
Our framework accommodates moderately high-dimensional vector-valued confounders and derives efficient influence functions for estimation, ensuring both robustness and interpretability. We establish asymptotic properties of the cross-fitted estimators and employ conformal inference techniques for counterfactual outcome prediction. Validated in both simulation and real-world environmental application, our framework extends causal inference methodologies to complex data structures, broadening its applicability across scientific disciplines.
