摘要
为了得到单纯形域内的二阶混料指数模型下的D-最优设计,首先,使用单纯形格点设计作为支撑点集,推导出二阶指数混料模型的信息矩阵及相关矩阵;其次,得到3分量与4分量情形下方差函数的具体形式,计算出D-最优设计的最优测度;然后,证明了在二阶格点支撑点集下的等测度设计是D-最优的;最后,比较3分量与4分量情形下的效率函数,D-最优设计效率变化相对稳定且效率较高.
In order to obtain the D-optimal design under the second-order mixture exponential model in the simplex region,first-ly,the simplex lattice design was used as the support point set to derive the information matrix and correlation matrix of the see-ond-order exponential mixture model;secondly,the specific form of the variance function under the 3-component and 4-compo-nent scenarios was obtained,the optimal measure of the D-optimal design was calculated,and then,it was proved that the equimeasures design under the second-order lattice support point set was D-optimal;finally,the efficieney functions under the 3-component and 4-component scenarios were compared,and the efficiency of the D-optimal design changed relatively stably and relatively high.
作者
李光辉
冯鑫
李俊鹏
LI Guanghui;FENG Xin;LI Junpeng(School of Microelectronics and Artificial Intelligence,Kaili University,Kaili 556011,China;School of Mathematics and Statistics,Jishou University,Jishou 416000,China;School of Science,Kaili University,Kaili 556011,China)
出处
《西南民族大学学报(自然科学版)》
2025年第5期550-559,共10页
Journal of Southwest Minzu University(Natural Science Edition)
基金
国家自然科学基金青年项目(11901260)
贵州省科学技术基金(黔科合基础[2020]1Y010)
凯里学院博士专项课题(BS201807)。
关键词
混料指数模型
D-最优设计
效率函数
Mixture exponential model
D-optimal design
efficiency function
