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

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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.