Unified Distributional Balancing for Causal Inference via Characteristic Function Distance

Thomas M. Menino Convention & Exhibition Center 

Weighting methods are widely used to estimate causal effects in observational studies by balancing pre-treatment covariates across treatment groups. Traditional approaches, such as inverse propensity score weighting or moment matching, achieve balance only indirectly and do not ensure alignment of full joint covariate distributions. Recently proposed distributional balancing methods offer flexible, nonparametric alternatives that directly target entire covariate distributions, but they lack a unified framework, theoretical guarantees, and valid inference procedures. We introduce a unified framework for nonparametric distributional balancing based on characteristic function distance (CFD), showing that popular discrepancies such as maximum mean discrepancy and energy distance arise as special cases. We establish conditions under which the resulting CFD-based weighting estimator is √n-consistent. Because the standard bootstrap may fail, we propose subsampling for valid inference. We further extend the framework to instrumental variable settings to address unmeasured confounding. Simulation and real-data analysis demonstrate strong empirical performance consistent with our theory.

Energy distance

Local average treatment effect

Maximum mean discrepancy

Reproducing kernel Hilbert space

Quadratic programming

Subsampling 

Section on Statistics in Epidemiology