Conditions for optimality in experimental designs

The purpose of this paper is to establish some results on optimal criteria in experimental designs. Some relationships between optimality criteria are shown. In particular, we extend results on the Phi(p) criteria. We prove the Yeh [Biometrika 73 (1986) 701] conjecture that gives a necessary and sufficient condition for a design to be universally optimal. We also give a similar result based on the eigenvalues of the information matrix. (C) 2004 Published by Elsevier Inc.