This paper introduces a robust estimation strategy for the spatial functional linear regression model using dimension reduction methods, specifically functional principal component analysis (FPCA) and functional partial least squares (FPLS). These techniques are designed to address challenges associated with spatially correlated functional data, particularly the impact of outliers on parameter estimation. By projecting the infinite-dimensional functional predictor onto a finite-dimensional space defined by orthonormal basis functions and employing M-estimation to mitigate outlier effects, our approach improves the accuracy and reliability of parameter estimates in the spatial functional linear regression context. Simulation studies and empirical data analysis substantiate the effectiveness of our methods, while an appendix explores the Fisher consistency and influence function of the FPCA-based approach. The rfsac package in R implements these robust estimation strategies, ensuring practical applicability for researchers and practitioners.

翻译：本文提出了一种利用降维方法（特别是函数主成分分析（FPCA）和函数偏最小二乘法（FPLS））的空间函数线性回归模型的稳健估计策略。这些技术旨在解决与空间相关函数数据相关的挑战，特别是异常值对参数估计的影响。通过将无限维函数预测变量投影到由正交基函数定义的有限维空间，并采用M估计来减轻异常值效应，我们的方法提高了空间函数线性回归背景下参数估计的准确性和可靠性。模拟研究和实证数据分析证实了我们方法的有效性，同时附录探讨了基于FPCA方法的Fisher相合性和影响函数。R语言中的rfsac包实现了这些稳健估计策略，确保了研究人员和实践者的实际适用性。