Optimal exact designs on a circle or a circular arc

• 成果类型: Article
• 署名作者: Wu, HQ
• 署名单位: University of Michigan System; University of Michigan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1069362385
• 发表日期: 1997
• 页码: 2027-2043
• 关键词: algorithms

摘要

Fitting a circle to a set of data points on a plane is very common in engineering and science. An important practical problem is how to choose the locations of measurement on a circular feature. So far little attention has been paid to this design issue and only some simulation results are available. Ill this paper, for Berman's bivariate four-parameter model, Phi-optimality is defined and shown to be equivalent to all phi(p)-criteria with p epsilon [-infinity, 1]. Then Phi-optimal exact designs on a circle or a circular are are derived for any sample size and sampling range. As a by-product, Phi-optimal approx;mate designs are also obtained. These optimal designs are used to evaluate the efficiency of the equidistant sampling method widely used in practice. These results also provide guidelines for users on sampling method and sample size selection.