General Equivalence Theory for Optimum Designs (Approximate Theory)
For general optimality criteria $\Phi$, criteria equivalent to $\Phi$-optimality are obtained under various conditions on $\Phi$. Such equivalent criteria are useful for analytic or machine computation of $\Phi$-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 $\Phi$, and for computing the equivalent criteria, are illustrated.
Permanent link to this document: http://projecteuclid.org/euclid.aos/1176342810
Digital Object Identifier: doi:10.1214/aos/1176342810
Mathematical Reviews number (MathSciNet): MR356386
Zentralblatt MATH identifier: 0291.62093