二阶Scheffé混料模型的E-最优设计  

E-Optimal Design for the Second-Order Scheffé Mixture Model

作　　者：陈嘉丽 凌羚 李俊鹏 张崇岐 CHEN Jia-li;LING Ling;LI Jun-peng;ZHANG Chong-qi(School of Economics and Statistics,Guangzhou University,Guangzhou 510006,China)

机构地区：[1]广州大学经济与统计学院,广东广州510006

出　　处：《数理统计与管理》2024年第5期856-864,共9页Journal of Applied Statistics and Management

基　　金：国家自然科学基金(12071096);广州大学研究生创新能力培养资助计划(2021GDJC-M01)。

摘　　要：混料试验设计在食品加工、化工制造及医药研发等领域有十分广泛的应用,比如一份好的试验设计方案在由新型冠状病毒引起的肺炎COVID-19的疫苗研制过程中发挥着事半功倍的作用。在混料试验设计中,Scheffé中心多项式模型因有较强的实际应用价值而被广泛研究。本文主要研究了q分量二阶Scheffé中心多项式模型的E-最优设计,给出了该模型对应信息矩阵的最小特征根、E-最优设计及E-效率的显式表达式,并通过实例对所得最优设计在不同准则下的相对效率做出比较分析。Mixture experimental design has a wide range of applications in many fields,such as food processing,chemical manufacturing,and pharmaceutical research and development.For example,a good experimental design plays a multiplier role in the development of the vaccine for COVID-19,the novel coronavirus-caused pneumonia.The Scheffe central polynomial mixture model has been widely studied in the mixture experimental design because of its strong practical significance.In this paper,E-optimal design for the q-components second-order Scheffécentral polynomial mixture model is discussed.The explicit expressions of the minimum eigenvalue of the information matrix,E-optimal design and E-efficiency of the model are determined,and the relative efficiency of the optimal design under different criteria is compared and analyzed by an example.

关 键 词：混料试验 Scheffé模型 E-最优设计 效率 

分 类 号：O212[理学—概率论与数理统计] O212.6[理学—数学]