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 ex- perimental 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 multi-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 pro jects for three diﬀerent topics.
In the ﬁrst pro ject, 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 work are done case by case. So we propose a uniﬁed way of ﬁnding optimal designs for a class of models under general optimality criteria. In the second pro ject, 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 multi-covariate models under independent data. We are unable to ﬁnd the close-form solution