Spatial Homogeneity Learning Models with Applications to Socioeconomic Problems

这一研究项目将开发统计方法和相关理论，以促进社会经济问题的空间数据分析。该项目的动机是在许多现代数据集中发现的共同特征，如美国人口普查局的美国社区调查、美国经济分析局的数据和县健康排名和路线图数据。这些公共使用的数据集是巨大的，在不同的空间位置和不同的时间段，许多不同的人口和经济指标具有隐藏的同质性特征。该项目将提供一个通用公式和一个灵活的机器学习工具箱，用于探索潜在的异质性和分组，并发现空间数据分组中的隐藏模式。将招募学生，特别是从代表性不足的群体中招募学生参与研究。将开发有关时空统计和地理信息系统的新课程和方便用户使用的软件包。该项目将推进统计科学领域的知识，研究成果将对政府机构的工作有价值。该研究项目将开发一种地理自适应凹融合惩罚(GACP)学习方法，可以同时估计模型参数和恢复潜在隶属度。在GACP学习的基础上，该项目将进行三个具体的研究主题，新开发的方法将应用于不同的社会经济问题。在第一个主题中，该项目将为具有潜在分组结构的空间变化系数模型开发一种基于GACP学习的广义优化估计方法。在第二个专题中，该项目将把新开发的框架扩展到成分协变量，以探讨部门间国内生产总值贡献对美国次区域基尼系数的异质性影响。在第三个主题中，该项目将推导出美国不同州的洛伦兹曲线的联合估计和聚类程序。该项目将为新开发的估计量建立一致性和渐近分布，并将开发高效的ff优化算法。这个项目将推进社会经济问题的空间异质性学习的前沿。从这项研究中获得的知识将有助于区域经济政策和其他复杂的社会经济问题。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This research project will develop statistical methodologies and associated theories that facilitate the analysis of spatial data for socioeconomic problems. The project is motivated by common features found in many modern datasets, such as the U.S. Census Bureau's American Community Survey, data from the U.S. Bureau of Economic Analysis, and County Health Rankings & Roadmaps data. These public-use datasets are enormous and have hidden homogeneity features on many different demographic and economic indicators, at different spatial locations and different time periods. This project will provide a general formulation and a flexible machine learning toolbox for exploring latent heterogeneity and subgroups and discovering hidden patterns within subgroups of spatial data. Students will be recruited, especially from underrepresented groups, to participate in the research. New courses on spatio-temporal statistics and geographic information systems and user-friendly software packages will be developed. The project will advance knowledge within the statistical sciences, and the research results will be of value to the work of government agencies.This research project will develop a geographically adaptive concave fusion penalized (GACP) learning method that can simultaneously estimate the model parameters and recover the latent memberships. Based on the GACP learning, the project will pursue three specific research topics, and the newly developed methodology will be applied to different socioeconomic problems. In the first topic, the project will develop a generalized optimization estimation approach based on the GACP learning for spatially varying coefficient models with a latent grouping structure. In the second topic, the project will extend the newly developed framework to compositional covariates to explore heterogeneous effects of Intersectoral Gross Domestic Product contributions on Gini coefficients over subregions in the United States. In the third topic, the project will derive a joint estimation and clustering procedure of Lorenz curves across different states in the US. The project will establish consistency and asymptotic distributions for the newly developed estimators and will develop efficient algorithms for optimization. This project will advance the frontiers of spatial heterogeneity learning for socioeconomic problems. The knowledge gained from this research will benefit regional economic policy and other complex socioeconomic problems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.