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August 2013 Robust $T$-optimal discriminating designs
Holger Dette, Viatcheslav B. Melas, Petr Shpilev
Ann. Statist. 41(4): 1693-1715 (August 2013). DOI: 10.1214/13-AOS1117

Abstract

This paper considers the problem of constructing optimal discriminating experimental designs for competing regression models on the basis of the $T$-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 57–70]. $T$-optimal designs depend on unknown model parameters and it is demonstrated that these designs are sensitive with respect to misspecification. As a solution to this problem we propose a Bayesian and standardized maximin approach to construct robust and efficient discriminating designs on the basis of the $T$-optimality criterion. It is shown that the corresponding Bayesian and standardized maximin optimality criteria are closely related to linear optimality criteria. For the problem of discriminating between two polynomial regression models which differ in the degree by two the robust $T$-optimal discriminating designs can be found explicitly. The results are illustrated in several examples.

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Holger Dette. Viatcheslav B. Melas. Petr Shpilev. "Robust $T$-optimal discriminating designs." Ann. Statist. 41 (4) 1693 - 1715, August 2013. https://doi.org/10.1214/13-AOS1117

Information

Published: August 2013
First available in Project Euclid: 5 September 2013

zbMATH: 1277.62188
MathSciNet: MR3127846
Digital Object Identifier: 10.1214/13-AOS1117

Subjects:
Primary: 62K05

Keywords: Chebyshev polynomial , linear optimality criteria , model discrimination , optimal design , robust design

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 4 • August 2013
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