Abstract

Many experiments are designed to estimate as precise as possible the fixed parameters in the required models. For example, D-optimum designs ensure that the volume of the confidence ellipsoid for these parameters is minimized. In some cases, only some of the fixed parameters are of interest. DS-optimality is then required. However, little attention has been given to the accuracy of the estimation of the variance components in the models, while they are very important for the interpretation of the results and in some cases it is their estimation that is the reason for the studies to be carried out. We give examples of such studies and focus on the design of experiments where only the variance components are important. The resulting DV-optimum designs are useful to use in crossed or split-plot validation experiments where fixed effects can be regarded as nuisance parameters. We conclude with some considerations about the implications of our results on the design of experiments where both the fixed parameters and the variance components are important.