Construction and Applications of Simultaneous Confidence Bands for Linear Regression Models

Regression analysis is one of the most commonly employed statistical techniques. It has applications in all scientific areas, such as engineering, physics, chemistry, biology, finance, and medicine. Simultaneous confidence bands for regression models can be used not only to assess the plausible range of a regression model but also to gain quantitative information about the possible differences between different regression models. So the methodology of simultaneous confidence bands is an integral part of regression analysis and has immediate applications to data analysis.The proposed research is to study the construction of optimal confidence band which provides the most accurate information about a regression model under certain recently proposed optimality criterion, and to study ways of constructing simultaneous confidence bands of exact 1-a level for assessing the all-contrast differences of several regression model under some very general setting.