Optimal designs for mixed models in experiments based on ordered units

• 成果类型: Article
• 署名作者: Majumdar, Dibyen; Stufken, John
• 署名单位: University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University System of Georgia; University of Georgia
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS518
• 发表日期: 2008
• 页码: 1090-1107
• 关键词: free block-designs; CONSTRUCTION; TRENDS; EXISTENCE

摘要

We consider experiments for comparing treatments using units that are ordered linearly over time or space within blocks. In addition to the block effect, we assume that a trend effect influences the response. The latter is modeled as a smooth component plus a random term that captures departures from the smooth trend. The model is flexible enough to cover a variety of situations; for instance, most of the effects may be either random or fixed. The information matrix for a design will be a function of several variance parameters. While data will shed light on the values of these parameters, at the design stage, they are unlikely to be known, so we suggest a maximin approach, in which a minimal information matrix is maximized. We derive maximin universally optimal designs and study their robustness. These designs are based on semibalanced arrays. Special cases correspond to results available in the literature.