Assessing the Statistical Quality of Eigenvector Spatial Filter-Based Estimators

本项目研究线性回归背景下特征向量空间滤波(ESF)方法的性质。虽然ESF作为一种解决地理参考数据中潜在的空间自相关性的技术已经变得越来越流行，但基于ESF的回归模型估计器的质量还没有得到彻底的研究。需要评估的ESF估计量的统计性质包括无偏性、有效性、一致性和稳健性。这种基于ESF的估计者的质量评估可以支持ESF方法的有效性，证明它为使用线性回归分析地理参考数据提供了坚实的基础。基于ESF的估计中的多重测试校正是另一个尚未得到充分研究的领域。这将有助于填补文献中的这一空白，并推动特征向量空间滤波在线性回归中的应用。本项目将促进对ESF的了解和理解，ESF是最近发展起来的一种地理参考数据统计建模方法。对无偏、效率、一致性和稳健性的评估对于确定基于ESF的估计器的可用性至关重要。该项目将为ESF的线性回归技术提供良好的方法学基础。这将允许ESF方法扩展到对非正常地理参考数据进行建模。项目成果将促进采用ESF方法的各个领域的研究能力，包括经济学、区域科学、流行病学和生态学。

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.