Mathematical Sciences: Hierarchical and Empirical Bayes Analysis in Survey Sampling, Linear Models and Quality Assurance

本统计研究项目使用层次贝叶斯和经验贝叶斯方法在两种嵌套回归模型之间进行选择，以估计响应函数。估计量作为基于完整模型和简化模型的最小二乘估计量的加权平均值，其权重依赖于数据。如果观察到的比率表明是一个完整的模型，这些估计器更倾向于基于完整模型的最小二乘估计器，如果相反，则倾向于基于简化模型的最小二乘估计器。这个项目是在统计和概率的一般领域，并在调查抽样，线性模型和质量保证领域应用层次和经验贝叶斯方法。在抽样调查中，研究的重点是小面积估计。在这种情况下，从个别地区通常可以获得几个例子，并且可以通过合并来自类似邻近地区的信息来改进对某一地区或同时对几个地区感兴趣的参数的估计。

This statistics research project uses hierarchical and empirical Bayes methods to choose between two nested regression models for estimating the response function. The estimators serve as a weighted average of the least squares estimators based on the full and the reduced models with weights being dependent on the data. These estimators lean more toward the least squares estimators based on the full models if the observed ratio suggests a full model, and towards the least squares estimators based on the reduced model if the opposite is true. This project is in the general area of statistics and probability and applies hierarchical and empirical Bayes methods in areas of survey sampling, linear models, and quality assurance. In sample surveys, the research focuses on small area estimation. In such cases, typically a few examples are available from an individual area, and estimates of parameters of interest for a certain area or simultaneously for several areas can be improved by incorporating information from similar neighboring areas.