Nonparametric Causal Inference with Functional Covariates
针对协变量包含函数型变量的情况，提出逆概率加权估计量来估计平均处理效应，并证明了估计量的根号n一致性和渐近正态性，通过数值实验和实证应用展示了方法的有效性。
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.