The Annals of Statistics

Optimal discriminating designs for several competing regression models

Dietrich Braess and Holger Dette

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Abstract

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

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

Dates
First available in Project Euclid: 29 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.aos/1369836964

Digital Object Identifier
doi:10.1214/13-AOS1103

Mathematical Reviews number (MathSciNet)
MR3099125

Zentralblatt MATH identifier
1360.62412

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

Keywords
Optimal design model discrimination vector-valued approximation

Citation

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. https://projecteuclid.org/euclid.aos/1369836964


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References

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