标题： 基于核的方法估计函数因果效应 显示英文标题

标题： Kernel-based estimators for functional causal effects

摘要： 我们提出了基于经验Fréchet均值和算子值核的因果效应估计器，专门针对函数数据空间。 这些方法解决了高维性、序列排序和模型复杂性的问题，同时保持了对治疗误设的鲁棒性。 利用结构假设，我们获得了潜在结果的紧凑表示，从而实现了时间上和协变量上的因果效应可扩展估计。 我们提供了关于函数因果效应一致性的理论分析以及多种提出的因果效应估计器的经验比较。 二元治疗设置中的应用展示了该框架在生物医学监测中的实用性，其中结果表现出复杂的时序动态。 我们的估计器可以处理具有注册协变量和结果的场景，并将其与Fréchet均值对齐，还可以处理需要更高阶表示以捕获复杂协变量-结果交互的情况。 这些进展将因果推断扩展到动态和非线性领域，为理解函数数据设置中的复杂治疗效应提供了新的工具。 显示英文摘要

摘要： We propose causal effect estimators based on empirical Fr\'{e}chet means and operator-valued kernels, tailored to functional data spaces. These methods address the challenges of high-dimensionality, sequential ordering, and model complexity while preserving robustness to treatment misspecification. Using structural assumptions, we obtain compact representations of potential outcomes, enabling scalable estimation of causal effects over time and across covariates. We provide both theoretical, regarding the consistency of functional causal effects, as well as empirical comparison of a range of proposed causal effect estimators. Applications to binary treatment settings with functional outcomes illustrate the framework's utility in biomedical monitoring, where outcomes exhibit complex temporal dynamics. Our estimators accommodate scenarios with registered covariates and outcomes, aligning them to the Fr\'{e}chet means, as well as cases requiring higher-order representations to capture intricate covariate-outcome interactions. These advancements extend causal inference to dynamic and non-linear domains, offering new tools for understanding complex treatment effects in functional data settings.