General Equivalence Theory for Optimum Designs (Approximate Theory)

For general optimality criteria Φ, criteria equivalent to Φ-optimality are obtained under various conditions on Φ. Such equivalent criteria are useful for analytic or machine computation of Φ-optimum designs. The theory includes that previously developed in the case of D-optimality (Kiefer-Wolfowitz) and L-optimality (Karlin-Studden-Fedorov), as well as E-optimality and criteria arising in response surface fitting and minimax extrapolation. Multiresponse settings and models with variable covariance and cost structure are included. Methods for verifying the conditions required on Φ, and for computing the equivalent criteria, are illustrated.