AI 中文总结
本文提出SpatialFoFReg R包实现的空间函数-函数分位数回归框架，通过函数型空间自回归结构与两阶段工具变量法，在PM₂.₅等数据上表现优于非空间及均值模型，用于环境风险管理等领域。
AI 中文摘要
本文提出了一种新颖的惩罚型空间函数-函数分位数回归框架，用于分析空间索引的函数型数据，填补了空间函数模型与分位数回归之间的关键空白。本研究有三项核心贡献：其一，我们提出了首个空间函数-函数分位数回归模型，该模型通过函数型空间自回归结构联合考虑曲线间的空间相关性，同时支持对函数型响应的任意条件分位数进行推断；与传统基于均值的替代方法不同，此方法可成功捕捉超出条件均值的状态依赖波动性与分布动态。其二，我们开发了两阶段工具变量估计策略，以解决函数型空间滞后引发的内生性问题；通过采用张量积B样条展开结合张量积粗糙度惩罚，我们的方法在避免主成分截断固有信息损失的同时，确保了最优平滑性。其三，对于固定样条维度，我们建立了样条系数估计量的√n渐近正态性，以及重构系数曲面的诱导有限秩高斯过程极限。大量蒙特卡洛实验与对意大利PM₂.₅空气质量数据的高分辨率分析表明，空间函数-函数分位数回归显著优于非空间及基于均值的竞争方法，为环境风险管理与复杂函数型数据分析提供了稳健且具信息价值的工具。该方法已在SpatialFoFReg R包中实现。
英文摘要
This paper introduces a novel penalized spatial function-on-function quantile regression framework for analyzing spatially indexed functional data, bridging a critical gap between spatial functional models and quantile regression. Our work makes three key contributions. First, we propose the first spatial function-on-function quantile regression model that jointly accounts for spatial correlation across curves through a functional spatial autoregressive structure while allowing inference on arbitrary conditional quantiles of the functional response. Unlike traditional mean-based alternatives, this approach successfully captures state-dependent volatility and distributional dynamics beyond the conditional mean. Second, we develop a two-stage instrumental-variable estimation strategy to address endogeneity induced by the functional spatial lag. By utilizing tensor-product B-spline expansions with tensor-product roughness penalties, our method ensures optimal smoothness without the destructive information loss inherent in principal component truncation. Third, for fixed spline dimensions, we establish $\sqrt n$-asymptotic normality of the spline coefficient estimators and the induced finite-rank Gaussian-process limits for the reconstructed coefficient surfaces. Extensive Monte Carlo experiments and a high-resolution analysis of Italian PM$_{2.5}$ air quality data demonstrate that spatial function-on-function quantile regression significantly outperforms non-spatial and mean-based competitors, providing a robust and informative tool for environmental risk management and complex functional data analysis. Our method has been implemented in the SpatialFoFReg R package.
Comments56 pages, 7 figures
