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

在过去20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距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选民都对不同社区之间持续存在的不平等趋势表示持续关注。 如今，对定量工具的需求越来越大，以分析来自高通量源的这种差异信息。 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在分析此类数据时往往会掩盖重要特征。 因此，通过开发复杂的统计工具，可以从复杂的数据源中提取显著特征，从而更好地理解对差异的探索。 本项目将探索创新的多层次建模技术，以开发在科学上更有效和更有意义的措施。 具体而言，该研究将开发新的小面积估计模型和估计技术，包括均值-方差关系，分布鲁棒性和使用分层和非参数贝叶斯方法的多重比较。 此外，一些估计方程的方法将被开发来研究社会人口和社会经济变量与癌症发病率之间的关联，通过多层次广义线性模型。 该方法适用于高维稀疏数据的分析，统计学的发展将丰富多维小区域估计技术。 基于Dirichlet过程的鲁棒建模将促进聚类在社会经济数据分析背景下的研究。 多重比较程序将增强分层建模背景下的同时推理文献。 这些方法也将对其他研究领域产生影响，如教育、流行病学和遗传学。 此外，该项目将有助于研究生的研究培训，并促进跨学科合作。

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.