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

数学科学：调查抽样、线性模型和质量保证中的分层和经验贝叶斯分析

• 批准号: 8901334
• 负责人: Malay Ghosh
• 金额: $ 8.5万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-05-15 至 1993-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901334&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Hierarchical; Empirical; Bayes

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.

本统计研究项目使用分层贝叶斯方法和经验贝叶斯方法在两种嵌套回归模型中进行选择，以估计响应函数。估计器用作基于完全模型和简化模型的最小二乘估计器的加权平均，其中权重取决于数据。如果观察到的比率表明完全模型，则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分层和经验贝叶斯方法。在抽样调查中，研究重点放在小面积估计上。在这种情况下，通常可以从单个地区获得几个例子，并且可以通过结合来自相似邻近地区的信息来改进对某一地区或同时针对几个地区的感兴趣参数的估计。