## The Annals of Statistics

### General Equivalence Theory for Optimum Designs (Approximate Theory)

J. Kiefer

#### Abstract

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.

#### Article information

Source
Ann. Statist. Volume 2, Number 5 (1974), 849-879.

Dates
First available in Project Euclid: 12 April 2007

http://projecteuclid.org/euclid.aos/1176342810

Digital Object Identifier
doi:10.1214/aos/1176342810

Mathematical Reviews number (MathSciNet)
MR356386

Zentralblatt MATH identifier
0291.62093

JSTOR