A New Approach to Optimal Design for Linear Models With Correlated Observations

• 成果类型: Article
• 署名作者: Zhigljavsky, Anatoly; Dette, Holger; Pepelyshev, Andrey
• 署名单位: Cardiff University; Ruhr University Bochum; University of Sheffield
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2010.tm09467
• 发表日期: 2010
• 页码: 1093-1103
• 关键词: long-range dependence; regression problems; time; Robustness

摘要

We consider the problem of designing experiments for regression in the presence of correlated observations with the location model as the main example. For a fixed correlation structure approximate optimal designs are determined explicitly, and it is demonstrated that under the model assumptions made by Bickel and Herzberg (1979) for the determination of asymptotic optimal design, the designs derived in this article converge weakly to the measures obtained by these authors. We also compare the asymptotic optimal design concepts of Sacks and Ylvisaker (1966, 1968) and Bickel and Herzberg (1979) and point out some inconsistencies of the latter. Finally, we combine the best features of both concepts to develop a new approach for the design of experiments for correlated observations, and it is demonstrated that the resulting design problems are related to the (logarithmic) potential theory.