Enhancing Spatial Functional Linear Regression with Robust Dimension Reduction Methods

TL;DR

This paper develops a robust estimation approach for spatial functional linear regression models by integrating dimension reduction techniques like FPCA and FPLS with M-estimation, effectively handling outliers in spatially correlated functional data.

Contribution

It introduces a novel robust estimation framework combining dimension reduction and M-estimation for spatial functional linear regression, addressing outlier sensitivity.

Findings

Improved parameter estimation accuracy demonstrated through simulations.

Effective outlier mitigation in empirical data analysis.

Implementation available via the rfsac R package.

Abstract

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.