Optimal design of experiments
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In design of experiments, optimal designs are designs that can glean the maximal amount of information from a study. Therefore, an optimal design can reduce the number of experimental units needed and saving the cost of study. However, the research in designing optimal experiments has not kept up with the increasingly complicated structure of data and models; especially for correlated data and multiple-covariate models, finding optimal designs is very difficult. In a series of papers by Yang and Stufken, the complete class approach has been revitalized by applying it to the optimal design problem with great success. Their inspirational idea has spawned my research, which includes three projects for three different topics. In the first project, we develop a general approach to find optimal designs for independent data with a single covariate. There has been lots of research under this topic, but most of the work is done on a case by case basis. So we propose a unified way of finding optimal designs for a class of models under general optimality criteria. In the second project, we consider correlated data with a single covariate. There are very few results under this topic. To bridge the gap, we extend the result from independent data to correlated data. Finally, we consider multiple-covariate models under independent data. We are unable to find closed-form solutions for optimal designs, but we give a complete class result that can save the computational resources by orders of magnitude.