Computation of c-optimal designs for models with correlated observations

In the optimal design of experiments setup, different optimality criteria can be considered depending on the objectives of the practitioner. One of the most used is c-optimality, which for a given model looks for the design that minimizes the variance of the linear combination of the parameters’ estimators given by vector c. c-optimal designs are needed when dealing with standardized criteria, and are specially useful when c is taken to be each one of the Euclidean vectors since in that case they provide the best designs for estimating the individual parameters. The well known procedure proposed by Elfving for independent observations is the origin of the procedure that can be used in the correlation framework. Some analytical results are shown for the model with constant covariance, but even in this case the computational task can become quite hard. For this reason, an algorithmic procedure is proposed; it can be used when dealing with a general model and some covariance structures.