# Enhancing Spatial Functional Linear Regression with Robust Dimension Reduction Methods

**Authors:** Ufuk Beyaztas, Abhijit Mandal, Han Lin Shang  
**arXiv:** [2410.19140](https://arxiv.org/abs/2410.19140)  
**Date:** 2024-10-24  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2410.19140v1/

## Key points

- Introduction of a robust estimation strategy for spatial functional linear regression model using dimension reduction methods
- Utilization of functional principal component analysis (FPCA) and functional partial least squares (FPLS) to handle challenges with spatially correlated functional data and outliers
- Projection of infinite-dimensional functional predictor onto a finite-dimensional space defined by orthonormal basis functions
- Employment of M-estimation to mitigate outlier effects and improve parameter estimation accuracy and reliability
- Exploration of spatial correlation and outlier analysis in U.S. COVID-19 data through local Moran's I statistic computation
- Construction of weight matrix based on inverse distances between cities using the Haversine formula
- Investigation of local indicators of spatial association to identify significant spatial clustering patterns
- Validation of method effectiveness through simulation studies and empirical data analysis
- Discussion on Fisher consistency and influence function of FPCA-based approach in an appendix
- Development of R package "rfsac" to implement robust estimation strategies for practical use by researchers and practitioners

## Summary

The paper "Enhancing Spatial Functional Linear Regression with Robust Dimension Reduction Methods" 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) are employed 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, this approach improves the accuracy and reliability of parameter estimates in the context of spatial functional linear regression. In this study, the authors delve into the spatial correlation and outlier analysis of U.S. COVID-19 data through the computation of local Moran's I statistic. They construct a weight matrix based on inverse distances between cities and calculate distances using the Haversine formula. The paper explores local indicators of spatial association to provide insight into significant spatial clustering of similar values. Simulation studies and empirical data analysis support the effectiveness of these methods in improving parameter estimation accuracy. An appendix in the paper also explores Fisher consistency and influence function of FPCA-based approach. The authors have developed an R package called rfsac that implements these robust estimation strategies, making them practical for researchers and practitioners in various fields. Overall, this research contributes valuable insights into enhancing spatial functional linear regression models through robust dimension reduction methods. It offers a comprehensive approach to address challenges related to outliers and spatial correlation in functional data analysis.