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Alphabetic optimality criteria, such as the $D$, $A$, and $I$ criteria,require specifying a model to select optimal designs. They are not model freeand the optimal designs selected by them are not robust to model uncertainty.Recently, many extensions of the $D$ and $A$ criteria have been proposed forselecting robust designs with high estimation efficiency. However, approachesfor finding robust designs with high prediction efficiency are rarely studiedin the literature. In this paper, we propose the $P_\alpha$ criterion anddevelop its approximation version for two-level designs, called the ${\tildeP_\alpha}$ criterion. They are useful for selecting robust designs with highestimation, high prediction, or balanced estimation and prediction efficiencyfor projective submodels. Computational studies show that the ${\tildeP}_\alpha$ criterion is a good approximation of the $P_\alpha$ criterion andcan reduce great computation time when we search designs over a wide range ofmodels. The connection between the ${\tilde P_\alpha}$ criterion and thegeneralized minimum aberration (GMA) criterion is studied. Result shows that${\tilde P_\alpha}$ plays a great role to link the alphabetic optimalitycriteria and the aberration-based criteria.

Robust designs to model uncertainty with high estimation and prediction efficiency