Nonparametric causal inference with functional covariates

Functional data and their analysis have become increasingly popular in various fields of data science. This article considers estimation and inference of the average treatment effect under unconfoundedness when the covariates involve a functional variable, and proposes the inverse probability weighting estimator, where the propensity score is estimated by using a kernel estimator for functional variables. We establish the √-consistency and asymptotic normality of the proposed estimator. Numerical experiments and an empirical application demonstrate the usefulness of the proposed method.