The Annals of Statistics

Optimal discriminating designs for several competing regression models

Dietrich Braess and Holger Dette

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The problem of constructing optimal discriminating designs for a class of regression models is considered. We investigate a version of the $T_{p}$-optimality criterion as introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 289–303]. The numerical construction of optimal designs is very hard and challenging, if the number of pairwise comparisons is larger than 2. It is demonstrated that optimal designs with respect to this type of criteria can be obtained by solving (nonlinear) vector-valued approximation problems. We use a characterization of the best approximations to develop an efficient algorithm for the determination of the optimal discriminating designs. The new procedure is compared with the currently available methods in several numerical examples, and we demonstrate that the new method can find optimal discriminating designs in situations where the currently available procedures fail.

Article information

Ann. Statist., Volume 41, Number 2 (2013), 897-922.

First available in Project Euclid: 29 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K05: Optimal designs
Secondary: 41A30: Approximation by other special function classes 41A50: Best approximation, Chebyshev systems

Optimal design model discrimination vector-valued approximation


Braess, Dietrich; Dette, Holger. Optimal discriminating designs for several competing regression models. Ann. Statist. 41 (2013), no. 2, 897--922. doi:10.1214/13-AOS1103.

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