Maximin designs for exponential growth models and heteroscedastic polynomial models

• 成果类型: Article
• 署名作者: Imhof, LA
• 署名单位: Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1009210553
• 发表日期: 2001
• 页码: 561-576
• 关键词: parameter nonlinear models; regression

摘要

This paper is concerned with nonsequential optimal designs for a class of nonlinear growth models, which includes the asymptotic regression model. This design problem is intimately related to the problem of finding optimal designs for polynomial regression models with only partially known heteroscedastic structure. In each case, a straightforward application of the usual D-optimality criterion would lead to designs which depend on the unknown underlying parameters. To overcome this undesirable dependence a maximin approach is adopted. The theorem of Perron and Frobenius on primitive matrices plays a crucial role in the analysis.