Techniques and applications of interval estimation

This dissertation consists of three papers written on different aspects of interval estimation. The first paper discusses interval estimation for assay response curves for nonlinear mixed models. It first discusses interval estimation in linear models, linear mixed models, and nonlinear models. This paper then extends the concept to nonlinear mixed models and how to appropriately calculate these intervals from software. An example is given on how to calculate the intervals. The second paper discusses the distribution of interval endpoints. Researchers in the pharmaceutical industry must do stability studies to determine or verify shelf life of a product; this is generally determined by an interval endpoint. Since these endpoints in themselves are random variables, it is of interest to see how they behave. Thus, the theoretical distribution is found as well as the asymptotic distribution. The third paper presents empirical methods of estimating the distribution of interval endpoints. This is of interest due to the numerical integration needed for the theoretical distribution. A Bayesian method as well as a bootstrap solution of estimating the distribution of interval endpoints is found