2013
DOI: 10.1214/13-aos1117
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Robust $T$-optimal discriminating designs

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 d… Show more

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Cited by 19 publications
(33 citation statements)
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“…This number is that obtained on theoretical grounds by Dette and Titoff [12] for T-optimal designs when all models of interest are polynomials. Case (8) in Table 2 has 7 parameters but leads to an optimal discrimination design with 5 support points.…”
Section: Resultsmentioning
confidence: 59%
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“…This number is that obtained on theoretical grounds by Dette and Titoff [12] for T-optimal designs when all models of interest are polynomials. Case (8) in Table 2 has 7 parameters but leads to an optimal discrimination design with 5 support points.…”
Section: Resultsmentioning
confidence: 59%
“…The T-optimal design maximizes the lack of fit sum of squares for the second model by maximizing the minimal lack of fit sum of squares arising from a set of plausible values of the unknown parameters. Additional theoretical developments can be found in Ponce de Leon and Atkinson [33], Dette [9], Fedorov and Hackl [16], Wiens [46] and Dette and Titoff [12]. López-Fidalgo et al [29] extend the method to models in which the errors of observation do not follow a normal distribution.…”
Section: Introductionmentioning
confidence: 99%
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“…The number of support points of the optimal design is not known a priori and so we used an iterative procedure to find it. Following Dette and Tittof (2009) [50], we set the number of support points, k , in the starting design equal to n p and solve the problem; if necessary we update the value of k and re-solve the problem until there is no improvement in the objective function for two consecutive values of k or one of the k support points of the design has a null weight. The latter strategy is inspired by the cutting plan algorithm to determine optimal designs of experiments [51].…”
Section: Global Optimization-generated Optimal Designsmentioning
confidence: 99%