Functional data analysis is an important area in modern statistics and has been successfully applied in many fields. Although many scientific studies aim to find causations, a predominant majority of functional data analysis approaches can only reveal correlations. In this paper, average treatment effect estimation is studied for observational data with functional covariates. This paper generalizes various state-of-art propensity score estimation methods for multivariate data to functional data. The resulting average treatment effect estimators via propensity score weighting are numerically evaluated by a simulation study and applied to a real-world dataset to study the causal effect of duloxitine on the pain relief of chronic knee osteoarthritis patients.

中文翻译：

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具有函数协变量的观察性研究中的平均治疗效果估计

泛函数据分析是现代统计学中的一个重要领域，并已成功应用于许多领域。尽管许多科学研究旨在寻找因果关系，但绝大多数功能数据分析方法只能揭示相关性。在本文中，研究了具有函数协变量的观测数据的平均治疗效果估计。本文将用于多变量数据的各种最先进的倾向得分估计方法推广到功能数据。通过倾向评分加权得到的平均治疗效果估计值通过模拟研究进行数值评估，并应用于真实世界的数据集，以研究度洛西汀对慢性膝关节骨关节炎患者疼痛缓解的因果影响。