Collaborative Research: Statistical Methods Based on Parametric and Semiparametric Hierarchical Models to Solve Problems Related to Socio-Economic-Demographic Deprivation Measures

在过去二十年左右的时间里，不同种族和经济背景的社区之间存在的差异受到了相当大的关注。学者、官僚、立法者、管理机构和许多其他成员都对不同社区之间持续存在的差距趋势感到担忧。今天，人们越来越需要定量工具来分析来自高通量来源的这种差异信息。在分析这些数据时，与社会经济、社会人口和社会健康剥夺措施有关的简单描述性统计数据往往会掩盖重要特征。因此，通过开发复杂的统计工具，从复杂的数据源中提取显著特征，可以更好地理解差异的探索。该项目将探索创新的多层次建模技术，以制定科学上更有效和有意义的措施。具体而言，研究将开发新的小区域估计模型和估计技术，包括均方差关系，分布稳健性和使用分层和非参数贝叶斯方法的多重比较。此外，将开发一些估计方程方法来研究社会人口和社会经济变量与癌症发病率之间的关系，通过多层次广义线性模型联系起来。该方法潜在地适用于分析高维和稀疏数据。统计的发展将丰富小面积估计技术的各个维度。基于Dirichlet过程的鲁棒建模将推动社会经济数据分析背景下的聚类研究。多重比较程序将增强分层建模背景下的同时推理文献。这些方法也将对教育、流行病学和遗传学等其他研究领域产生影响。此外，该项目将有助于以研究为基础的研究生培训和促进跨学科合作。

The existence of disparities among communities of diverse racial and economic backgrounds has received considerable attention in last two decades or so. Scholars, bureaucrats, legislators, governing bodies, and numerous other constituents share a sustained concern about the persistent trend of disparity across diverse communities. Today, there is an increasing demand for quantitative tools to analyze such disparity information from high-throughput sources. Simple descriptive statistics that relate to socio-economic, socio-demographic, and socio-health deprivation measures often can mask the important features while analyzing such data. Thus, the exploration of disparity can be better understood by developing sophisticated statistical tools that can extract the salient features from complex data sources. This project will explore innovative multilevel modeling techniques to develop measures that are scientifically more efficient and meaningful for these purposes. Specifically, the research will develop new small area estimation models and estimation techniques that encompass mean-variance relationship, distributional robustness, and multiple comparisons using hierarchical and nonparametric Bayesian approaches. Furthermore, some estimating equation approaches will be developed to study the association between socio-demographic and socio-economic variables with cancer incidence, linked via multilevel generalized linear models. The methods potentially are suitable for analyzing high-dimensional and sparse data.The statistical development will enrich small area estimation technique in various dimensions. The Dirichlet process-based robust modeling will advance the research on clustering in the context of analyzing socio-economic data. The multiple comparison procedures will enhance the simultaneous inference literature in the context of hierarchical modeling. The methods also will have implications in other areas of research such as education, epidemiology, and genetics. In addition, the project will contribute towards research-based training of graduate students and foster interdisciplinary collaboration.