Optimality criteria for regression models based on predicted variance

In the context of nonlinear regression models, a new class of optimum design criteria is developed and illustrated. This new class, termed I-L-optimality, is analogous to Kiefer's Phi(k)-criterion but is based on predicted variance, whereas Kiefer's class is based on the eigenvalues of the information matrix; I-L-optimal designs are invariant with respect to different parameterisations of the model and contain G- and D-optimality as special cases. We provide a general equivalence theorem which is used to obtain and verify I-L-optimal designs. The method is illustrated by various examples.