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November, 1976 Convergent Design Sequences, for Sufficiently Regular Optimality Criteria
Corwin L. Atwood
Ann. Statist. 4(6): 1124-1138 (November, 1976). DOI: 10.1214/aos/1176343647

Abstract

For an optimality criterion function $\Phi$ and a design $\xi_n$, approximate $\Phi(\mathbf{M}(\xi))$ near $\xi_n$ by a quadratic Taylor expansion, let $\xi_n + \eta$ minimize this approximation, and let $\xi_{n+1} = \xi_n + \alpha\eta$, with $\alpha$ minimizing $\Phi(\mathbf{M}(\xi_{n+1}))$. If $\Phi$ satisfies regularity conditions, including strict convexity, possession of three continuous derivatives, and finiteness only for nonsingular $\mathbf{M}$, then $\mathbf{M}(\xi_n)$ converges to the optimal value for both the Federov steepest descent sequence and the above quadratic sequence, with the quadratic sequence having a faster asymptotic convergence rate. Methods are discussed for collapsing clusters of design points during the iterative process. In a simple example with $D$-optimality, the two methods are comparable. In a more complicated example the quadratic method is far superior.

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Corwin L. Atwood. "Convergent Design Sequences, for Sufficiently Regular Optimality Criteria." Ann. Statist. 4 (6) 1124 - 1138, November, 1976. https://doi.org/10.1214/aos/1176343647

Information

Published: November, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0344.62064
MathSciNet: MR418352
Digital Object Identifier: 10.1214/aos/1176343647

Subjects:
Primary: 62K05
Secondary: 65B99

Keywords: $\phi$-optimality , $D$-optimality , $L$-optimality , generalized Newton method , Optimal experimental designs , steepest descent

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 6 • November, 1976
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