Clustered Coefficient Regression Model-Based Estimators in Small Area Estimation

本研究项目将开发基于模型的估计器，用于估计小区域的人口参数。小区域估计是抽样调查中的一个重要问题，当样本容量不足以在小区域或区域内提供可靠的估计时。在抽样调查中，为了提高估计量的精度，基于辅助变量的模型估计量被广泛应用。然而，如果感兴趣的变量和辅助变量之间存在异质关系，则基于同质性的传统模型将不能准确地描述这种关系。该项目将开发新的基于模型的估算器，其基础是更灵活的回归模型，称为聚类系数回归模型。新的估计器将应用于不同的国家调查，如美国人口普查局进行的美国社区调查。该项目的结果将作为抽样调查课程的范例。本科生和研究生都将参与这项研究项目。该研究项目将开发基于聚类系数回归模型的新的基于模型的估计器，该模型使用惩罚函数，也可以借用不同区域的空间或排序信息。该项目将弥合聚类系数回归和基于模型的估计之间的差距。本文将研究小区域估计中的三种类型的估计量。首先，该项目将为线性回归模型和逻辑回归模型开发基于聚类系数的新的广义回归估计。其次，该项目将研究基于聚集系数回归模型的新单位级估计量，包括当前线性模型的扩展以及考虑随机效应的二进制数据新估计量的开发。最后，该项目将开发基于聚类系数的新的区域水平估算器，包括基于beta回归模型的比例扩展。该奖项反映了NSF的法定使命，并被认为值得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来支持。

This research project will develop model-based estimators for estimating population parameters in small areas. Small area estimation is an important problem in survey sampling when the sample sizes are not large enough to provide reliable estimates in small areas or domains. Model-based estimators based on auxiliary variables are widely used to increase the precision of estimators in survey sampling. However, if a heterogeneous relationship exists between the variable of interest and auxiliary variables, traditional models based on homogeneity will not accurately describe the relationship. This project will develop new model-based estimators based on more flexible regression models called clustered coefficient regression models. The new estimators will be applied to different national surveys, such as American Community Survey conducted by the U.S. Census Bureau. Results from the project will be used as examples in a course on survey sampling. Both undergraduate and graduate students will be involved in the research project. Publicly available R packages also will be developed.This research project will develop new model-based estimators based on clustered coefficient regression models using penalty functions, which also can borrow spatial or ordering information in different areas. The project will bridge the gap between clustered coefficient regression and model-based estimators. Three types of estimators in small area estimation will be studied. First, the project will develop new generalized regression estimators based on clustered coefficients for both linear regression models and logistic regression models. Second, the project will examine new unit level estimators based on clustered coefficient regression models, including an extension of the current linear model and the development of new estimators for binary data with consideration of random effects. Finally, the project will develop new area level estimators based on clustered coefficients, including an extension to proportions based on beta regression models.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.