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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2017, Vol. 34 ›› Issue (1): 1-12.doi: 10.3969/j.issn.1005-3085.2017.01.001

• •    下一篇

异方差混料模型的直积设计及其最优性

燕   飞1,    张崇岐2,   

  1. 1- 北京师范大学珠海分校应用数学学院，珠海  519087 
    2- 广州大学经济与统计学院，广州  510006
  • 收稿日期:2014-08-15 接受日期:2016-09-08 出版日期:2017-02-15 发布日期:2017-04-15
  • 通讯作者: 张崇岐 E-mail: cqzhang@gzhu.edu.cn

Direct Product Design for Mixture Models with Heteroscedastic Errors and its Optimalities

YAN Fei1,   ZHANG Chong-qi2   

  1. 1- School of Applied Mathematics, Beijing Normal University (Zhuhai), Zhuhai 519087 
    2- School of Economics and Statistics, Guangzhou University, Guangzhou 510006
  • Received:2014-08-15 Accepted:2016-09-08 Online:2017-02-15 Published:2017-04-15
  • Contact: C. Zhang. E-mail address: cqzhang@gzhu.edu.cn

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摘要： 混料试验设计在工农业生产、科学试验以及日常生活中具有广泛的应用．传统的混料试验设计大都在试验误差同方差性的假设前提下进行，但是相对而言，试验误差异方差性更符合实际．针对这一问题，本文主要研究了在试验误差异方差性的假设条件下，混料乘积模型直积设计的$D$-、$A$-以及线性最优性问题．在给定条件下，通过构建混料齐次子模型的$D$-、$A$-或线性最优设计，可以证明其乘积模型的直积设计也是相应的最优设计．

关键词: 混料试验, 异方差性, 直积设计, $D$-最优性, $A$-最优性, 线性最优性

Abstract:


Mixture experimental designs have been widely used in industrial and agricultural production, scientific experiment and daily life. The traditional mixture experimental designs are generally implemented under the assumption that the experimental errors are homosce-dastic, but heteroscedastic errors are relatively more accordant with practical circumstances. In this paper, we mainly study the $D$-, $A$- and linear optimality of direct product designs for mixture product models under the assumption of heteroscedastic errors. It is shown that the $D$-, $A$- or linear optimal designs for mixture product models can be constructed from the corresponding optimal designs for their homogeneous sub-mixture models under given conditions.

Key words: mixture experiments, heteroscedasticity, direct product design, $D$-optimality, $A$-optimality, linear optimality

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