Spatial function-on-function quantile regression

2026-08-21

AI Summary

本文提出了一种新的空间函数对函数分位数回归框架，通过考虑曲线间的空间相关性来分析空间索引的功能数据，并采用两阶段工具变量估计策略处理内生性问题。

Abstract

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.

Problem

• spatial function-on-function
• quantile regression
• functional spatial autoregressive

Innovation

• spatial function-on-function quantile regression
• functional spatial autoregressive structure
• two-stage instrumental-variable estimation
• tensor-product B-spline expansions