多响应混料模型的D-和A-最优设计(英文)  

D-and A-optimal designs for mixture experiments with multiresponse models

作　　者：金红娣[1] 岳荣先[1] 

机构地区：[1]上海师范大学数理信息学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2008年第2期124-130,共7页Journal of Shanghai Normal University(Natural Sciences)

基　　金：NSFC grant(10671129);the Special Funds for Doctoral Authori-ties of Education Ministry(20060270002)

摘　　要：考虑多响应模型E(Yi(X)) =ηi(X) =fiT(X)βi(i =1,2) ,其中两个响应分别为Scheffé一阶和二阶模型.主要研究一类支撑点为各顶点X (1,0,…,0)和各棱中心X (1/2,1/2,0,…,0)的设计,根据D-和A-最优设计准则得到最优设计测度r1*和r2*.最后给出最优设计效率的一些数值结果,说明D-和A-最优设计在模型参数估计方面差别不大.The mulfiresponse models E（Yi（X） ） = ηi（X） = fi^T（X）βi（i = 1,2） are considered,where η1 and η2 are the Seheffe＇s linear model and quadratic model, respectively. D- and A-optimal designs are investigated in this paper. More precisely, we restrict ourselves to a particular type of design ξ^＊ whose support points are X←→（ 1,0,..., 1 0,... 0）, and X←→（1/2,1/2,0,…,0）and obtain the weights r1^＊ and r2^＊ according to the D- and the A-optimal design criteria The numerical results about the effieieneies of these optimal designs show that D- and A-optimal designs do not differ too much in some mixture experiments.

关 键 词：多响应 混料试验 D-和A-最优设计 设计效率 

分 类 号：O212.6[理学—概率论与数理统计]