The Annals of Statistics

Robust $T$-optimal discriminating designs

Holger Dette, Viatcheslav B. Melas, and Petr Shpilev

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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.

Article information

Ann. Statist., Volume 41, Number 4 (2013), 1693-1715.

First available in Project Euclid: 5 September 2013

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Zentralblatt MATH identifier

Primary: 62K05: Optimal designs

Optimal design model discrimination robust design linear optimality criteria Chebyshev polynomial


Dette, Holger; Melas, Viatcheslav B.; Shpilev, Petr. Robust $T$-optimal discriminating designs. Ann. Statist. 41 (2013), no. 4, 1693--1715. doi:10.1214/13-AOS1117.

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