Assessing the Statistical Quality of Eigenvector Spatial Filter-Based Estimators

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This project investigates the qualities of eigenvector spatial filtering (ESF) methodology in a linear regression context. Although ESF has become more popular as a technique for addressing spatial autocorrelation latent in georeferenced data, the quality of ESF-based estimators for regression models has not been thoroughly investigated. The statistical qualities of ESF-based estimators needing assessment include unbiasedness, efficiency, consistency, and robustness. Such a quality assessment of ESF-based estimators can bolster the efficacy of ESF methodology, documenting that it furnishes a solid foundation for analyzing georeferenced data with linear regression. Multiple testing corrections in ESF-based estimation is another area that has not been adequately investigated. The will help fill this gap in the literature and advance the utility of eigenvector spatial filtering for linear regression.This project will advance knowledge and understanding of ESF, which is a recently developed method for statistical modeling of georeferenced data. The assessment of unbiasedness, efficiency, consistency, and robustness is essential to determine the usability of the ESF-based estimators. This project will furnish sound fundamentals of the ESF methodology for linear regression techniques. This will permit ESF methodology to be extended to modeling non-normal georeferenced data. Project results will facilitate research capabilities across the range of fields that have adopted ESF methodology, including economics, regional science, epidemiology, and ecology.