多响应混料模型最优设计的基础定理  

Basic Theorem for Optimal Design of Multiresponse Mixture Model

作　　者：朱小渊 郝红花 张新风 张崇岐 ZHU Xiao-yuan;HAO Hong-hua;ZHANG Xin-feng;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》2023年第4期637-648,共12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(2019GDJC-D19)

摘　　要：等价定理是混料模型试验设计中最重要的定理之一,特别的D-和G-最优设计的等价定理结果尤为完美。在单响应模型中,一般连续设计与等配置设计的D-最优性等价定理都已经存在,在多响应模型中,一般连续设计的D-最优性等价定理与单响应基本一致,但是等配置设计的D-最优等价定理却和单响应并非一致,等配置的设计在实际应用中的实现优势显而易见。本文就此给出多响应下等配置设计的D-和G-最优性等价定理,并给出几个说明性例子。The equivalence theorem is the most important theorem of experimental design,and espe-cially the equivalence theorem of the D-and G-optimal design is perfect.In the single response,the D-optimal equivalence theorem of the continuous design and the equal allocation design already exist.In the multiresponse,the D-optimal equivalence theorem of the continuous design is consistent with the single response,however the D-optimal equivalence theorem of the equal allocation design different from the single response.The design of equal allocation is easy to operate in practical applications.In this paper,we investigate the equivalent theorem of D-optimal for multiresponse equal allocation design.The D-and G-optimal designs for multiresponse are illustrated by two examples.

关 键 词：多响应 混料试验 D-最优设计 等价定理 

分 类 号：O212[理学—概率论与数理统计] O212.6[理学—数学]