Model-robust RR-optimal designs in linear regression models

• We consider the robust optimal design problem for linear regression models.
• The R-optimality is extended to the model-robust version with respect to a class of candidate models.
• Generalization of Elfving’s theorem is proved for the model-robust R-optimal designs to describe the geometrical characterization.
• Equivalence theorem for model-robust R-optimality is presented which is later used to verify optimality of designs through few illustrative examples.

This paper considers an extension of RR-optimality to model-robust optimal design, where a prior probability is set on a class of candidate linear models. A generalization of Elfving’s theorem is proved, which gives a geometrical characterization of model-robust RR-optimal designs. An equivalence theorem is presented and used to check optimality of designs in a few illustrative examples.