多响应混料模型的R-最优设计  

R-Optimal Design of Multi-Response Mixture Model

作　　者：张新风 郝红花 李光辉[2] ZHANG Xinfeng;HAO Honghua;LI Guanghui(School of Economics and Statistics,Guangzhou University,Guangzhou 510006;School of Science,Kaili University,Kaili Guizhou 556011,China)

机构地区：[1]广州大学经济与统计学院,广州510006 [2]凯里学院理学院,贵州凯里556011

出　　处：《重庆师范大学学报（自然科学版）》2022年第2期103-110,共8页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.12071096);国家自然科学基金青年项目(No.11901260);广东省中医药局科学研究项目(No.20201198);贵州省科学技术基金(No.黔科合基础[2020]1Y010)。

摘　　要：【目的】研究分别具有一阶和二阶线性混料模型的两响应的R-最优设计。【方法】由于响应之间具有一定的相关性,在分析两个线性混料模型的R-最优设计时候发现与协方差矩阵有关,关于这类模型下最优设计的构造就变得比较复杂。在协方差矩阵未定的情况下,根据R-最优准则的定义给出了相关矩阵的对角线乘积的一般表达式。【结果】在给定协方差的情况下用两个具体的例子说明如何求解R-最优设计,并验证了例2满足多响应R-最优设计的等价定理。【结论】对于任意的两响应混料试验模型可以用提出的方法求R-最优设计。[Purposes]The R-optimal design with the first-order and the second-order linear mixture models is studied. [Methods] The correlation between the responses shows that the R-optimal design of two linear mixture models is related to the covariance matrix. It made the construction of optimal design under such models more complicated. In the undetermined covariance matrix, the general expression of the diagonal product of the correlation matrix is given according to the definition of the R-optimal criterion. [Findings] Two concrete examples illustrate how to solve the R-optimal design under the given covariance matrix, and the equivalence theorem of example 2 satisfying the multi-response. [Conclusions] For any two response mixture models, this method can be used to solve the R-optimal design.

关 键 词：多响应 混料试验 R-最优设计 等价定理 

分 类 号：O212.6[理学—概率论与数理统计]