Spatial Homogeneity Learning Models with Applications to Socioeconomic Problems

该研究项目将发展统计方法和相关理论，以促进对社会经济问题的空间数据的分析。该项目的动力来自许多现代数据集中的共同特征，如美国人口普查局的美国社区调查数据，美国经济分析局的数据，以及县健康排名和路线图数据。这些公共用途数据集非常庞大，在不同空间位置和不同时期的许多不同人口和经济指标上具有隐藏的同质性特征。该项目将提供一个通用公式和灵活的机器学习工具箱，用于探索潜在的异质性和子组，并发现空间数据子组中的隐藏模式。将招募学生，特别是来自代表性不足的群体的学生参与研究。将编制关于时空统计和地理信息系统的新课程和用户友好的软件包。该项目将促进统计科学领域的知识，研究结果将对政府机构的工作有价值。本研究将开发一种能够同时估计模型参数和恢复潜在隶属度的地理自适应凹融合惩罚（GACP）学习方法。在GACP学习的基础上，该项目将开展三个具体的研究课题，并将新开发的方法应用于不同的社会经济问题。在第一个主题中，该项目将开发一种基于GACP学习的广义优化估计方法，用于具有潜在分组结构的空间变化系数模型。在第二个专题中，该项目将把新开发的框架扩展到组成协变量，以探索美国各分区域的部门间国内生产总值贡献对基尼系数的异质影响。在第三个主题中，该项目将推导出美国不同州洛伦兹曲线的联合估计和聚类过程。该项目将为新开发的估计量建立一致性和渐近分布，并将开发有效的优化算法。该项目将推动社会经济问题的空间异质性学习的前沿。从本研究中获得的知识将有利于区域经济政策和其他复杂的社会经济问题。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.