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Biometrika 1999 86(1):93-106; doi:10.1093/biomet/86.1.93
© 1999 by Biometrika Trust
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Optimality criteria for regression models based on predicted variance

H DetteA1 and TE O'BrienA2

A1 Fakultätat für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany holger.dette@ruhr-uni-bochum.de A2 K-490.3.51, CIBA-GEIGY AG, Postfach CH-4002 Basel, Schweiz tim.obrien@bluewin.ch

In the context of nonlinear regression models, a new class of optimum design criteria is developed and illustrated. This new class, termed IL-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; 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 IL-optimal designs. The method is illustrated by various examples.

Keywords:Bayesian design; Invariance; Optimal design.


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