Optimality criteria for regression models based on predicted variance

Abstract

In the context of nonlinear regression models, a new class of optimum design criteria is developed and illustrated. This new class, termed Ι L -optimality, is analogous to Kiefer's Φ k -criterion but is based on predicted variance, whereas Kiefer's class is based on the eigenvalues of the information matrix; 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 Ι L -optimal designs. The method is illustrated by various examples. Keywords: Bayesian design; Invariance; Optimal design.