Clustered Coefficient Regression Model-Based Estimators in Small Area Estimation

这项研究项目将开发基于模型的估计器，用于估计小地区的人口参数。小区域估计是抽样调查中的一个重要问题，当样本量不足以在小区域或小区域内提供可靠的估计时。在抽样调查中，基于辅助变量的模型估计量被广泛用于提高估计量的精度。然而，如果感兴趣变量和辅助变量之间存在异质关系，传统的基于同质性的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计器，该估计器基于更灵活的回归模型，称为集群系数回归模型。新的估计值将应用于不同的全国性调查，例如美国人口普查局进行的美国社区调查。该项目的结果将在一门调查抽样课程中用作范例。本科生和研究生都将参与这个研究项目。这个研究项目将开发新的基于模型的估计器，该模型基于使用惩罚函数的聚类系数回归模型，它还可以借用不同区域的空间或排序信息。该项目将弥合集群系数回归和基于模型的估计器之间的差距。对小区域估计中的三种估计量进行了研究。首先，该项目将为线性回归模型和Logistic回归模型开发基于聚集系数的新的广义回归估计器。第二，该项目将审查基于集群式系数回归模型的新的单位水平估计器，包括扩展现有的线性模型，并开发考虑随机影响的二进制数据的新估计器。最后，该项目将开发基于聚集系数的新的区域水平估计器，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 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.