## The Annals of Statistics

### 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 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

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

Dates
First available in Project Euclid: 5 September 2013

https://projecteuclid.org/euclid.aos/1378386236

Digital Object Identifier
doi:10.1214/13-AOS1117

Mathematical Reviews number (MathSciNet)
MR3127846

Zentralblatt MATH identifier
1277.62188

Subjects
Primary: 62K05: Optimal designs

#### Citation

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. https://projecteuclid.org/euclid.aos/1378386236

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