ROBUST T-OPTIMAL DISCRIMINATING DESIGNS

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 dem...

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Bibliographic Details
Published in:The Annals of statistics 2013-08, Vol.41 (4), p.1693-1715
Main Authors: Dette, Holger, Melas, Viatcheslav B., Shpilev, Petr
Format: Article
Language:English
Subjects:
62K05
Bayesian analysis
Chebyshev polynomial
Design efficiency
Design of experiments
Design optimization
Experiment design
linear optimality criteria
Linear regression
Mathematical models
Mathematical moments
Mathematical vectors
Maximin
model discrimination
Musical intervals
Optimal design
Parameter estimation
Parametric models
Polynomials
Regression analysis
robust design
Studies
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Summary: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.
ISSN:0090-5364
2168-8966
DOI:10.1214/13-AOS1117