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

这个统计研究项目使用层次和 经验贝叶斯方法在两个嵌套回归之间进行选择 用于估计响应函数的模型。 了估计量 作为最小二乘估计量的加权平均值， 权值依赖于完全模型和简化模型 在数据上。这些估计值更倾向于最小二乘 基于完整模型的估计量， 建议一个完整的模型，并对最小二乘估计 如果相反，则基于简化模型。 该项目属于一般统计领域， 概率和应用层次和经验贝叶斯方法 在调查抽样、线性模型和质量方面， 保证。 在抽样调查中，研究主要集中在小区域 估计。 在这种情况下，通常有几个例子， 可从个别地区，和参数的估计， 对某个区域或同时对几个区域感兴趣 可以通过合并来自类似的 邻近地区。

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.