The Annals of Statistics
- Ann. Statist.
- Volume 2, Number 5 (1974), 849-879.
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.
Ann. Statist., Volume 2, Number 5 (1974), 849-879.
First available in Project Euclid: 12 April 2007
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Primary: 62K05: Optimal designs
Kiefer, J. General Equivalence Theory for Optimum Designs (Approximate Theory). Ann. Statist. 2 (1974), no. 5, 849--879. doi:10.1214/aos/1176342810. https://projecteuclid.org/euclid.aos/1176342810