MINIMAX DESIGNS IN LINEAR-REGRESSION MODELS

• 成果类型: Article
• 署名作者: DETTE, H; HEILIGERS, B; STUDDEN, WJ
• 署名单位: University of Augsburg; Purdue University System; Purdue University; University of Gottingen
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324453
• 发表日期: 1995
• 页码: 30-40
• 关键词: optimality; THEOREM

摘要

In the usual linear regression model we investigate the geometric structure of a class of minimax optimality criteria containing Elfving's minimax and Kiefer's phi(p)-criteria as special cases. It is shown that the optimal designs with respect to these criteria are also optimal for A'theta, where A is any inball vector (in an appropriate norm) of a generalized Elfving set. The results explain the particular role of the A- and E-optimality criterion and are applied for determining the optimal design with respect to Elfving's minimax criterion in polynomial regression up to degree 9.