ELFVING THEOREM FOR D-OPTIMALITY

• 成果类型: Article
• 署名作者: DETTE, H
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349149
• 发表日期: 1993
• 页码: 753-766
• 关键词: regression; designs; models

摘要

We consider a model robust version of the c-optimality criterion minimizing a weighted product with factors corresponding to the variances of the least squares estimates for linear combinations of the parameters in different models. A generalization of Elfving's theorem is proved for the optimal designs with respect to this criterion by an application of an equivalence theorem for mixtures of optimality criteria. As a special case an Elfving theorem for the D-optimal design problem is obtained. In the case of identical models the connection between the A-optimality criterion and the model robust criterion is investigated. The geometric characterizations of the optimal designs are illustrated by a couple of examples.