ROBUST T-OPTIMAL DISCRIMINATING DESIGNS

• 成果类型: Article
• 署名作者: Dette, Holger; Melas, Viatcheslav B.; Shpilev, Petr
• 署名单位: Ruhr University Bochum; Saint Petersburg State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1117
• 发表日期: 2013
• 页码: 1693-1715
• 关键词: regression; models; fit

摘要

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.