异方差可加混料模型的直和设计及其D-最优性  

Direct sum design and its D-optimality for additive mixture model with heteroscedasticity

作　　者：燕飞 李光辉[2] 张崇岐 YAN Fei;LI Guang-hui;ZHANG Chong-qi(School of Applied Mathematics,Beijing Normal University,Zhuhai,Zhuhai 519087,China;School of science,Kaili University,Kaili 556011,China;School of Economics and Statistics,Guangzhou University,Guangzhou 510006,China)

机构地区：[1]北京师范大学珠海分校应用数学学院,广东珠海519087 [2]凯里学院理学院,贵州凯里556011 [3]广州大学经济与统计学院,广东广州510006

出　　处：《高校应用数学学报（A辑）》2023年第2期127-136,共10页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(12071096);广东省普通高校青年创新人才类项目(2019KQNCX183)。

摘　　要：混料试验设计中,对试验误差的异方差性假设更符合实际应用.该文主要研究了两种异方差结构下,一般可加混料模型的直和设计及其D-最优性.在给定条件下,将可加混料模型分解成子模型,通过构建子模型的D-最优设计的直和,从而获得可加混料模型的D-最优设计,为构建复杂混料模型的D-最优设计提供了可靠的方法.The heteroscedasticity hypothesis of experimental error is more suitable for practical application in mixing experiment design.In this paper,the direct sum designs and their D-optimality for additive mixtures models with two heteroscedasticity structures are studied.Under certain condi-tions,D-optimal design for a general additive mixtures model is obtained by constructing the direct sum of two D-optimal designs for the sub-models,which are decomposed from the original additive mixtures model.It provides a practical method for constructing D-optimal design for complex mixture model.

关 键 词：混料试验 异方差 D-最优性 直和设计 

分 类 号：O212.6[理学—概率论与数理统计]