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.
Publié le : 1974-09-14
Classification:
Optimum experimental designs,
equivalence theory of designs,
$D$-optimality,
$A$-optimality,
$E$-optimality,
iterative design optimization,
large eigenvalues,
62K05
@article{1176342810,
author = {Kiefer, J.},
title = {General Equivalence Theory for Optimum Designs (Approximate Theory)},
journal = {Ann. Statist.},
volume = {2},
number = {1},
year = {1974},
pages = { 849-879},
language = {en},
url = {http://dml.mathdoc.fr/item/1176342810}
}
Kiefer, J. General Equivalence Theory for Optimum Designs (Approximate Theory). Ann. Statist., Tome 2 (1974) no. 1, pp. 849-879. http://gdmltest.u-ga.fr/item/1176342810/