‘Nearly’ universally optimal designs for models with correlated observations

The problem of determining optimal designs for least squares estimation is considered in the common linear regression model with correlated observations. The approach is based on the determination of ‘nearly’ universally optimal designs, even in the case where the universally optimal design does not exist. For this purpose, a new optimality criterion which reflects the distance between a given design and an ideal universally optimal design is introduced. A necessary condition for the optimality of a given design is established. Numerical methods for constructing these designs are proposed and applied for the determination of optimal designs in a number of specific instances. The results indicate that the new ‘nearly’ universally optimal designs have good efficiencies with respect to common optimality criteria.