平衡线性混合效应模型的最优设计  

Optimal Designs for Balanced Linear Mixed-Efects Regression Models

作　　者：周晓东[1] 岳荣先[2] 

机构地区：[1]上海对外经贸大学商务信息学院,上海201620 [2]上海师范大学数理学院,上海200234

出　　处：《应用概率统计》2013年第4期414-432,共19页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(11071168;11141002);上海对外经贸大学085工程项目(Z08512053);教育部高校博士点专项科研基金(20103127110002);上海市教委科研创新重点项目(11zz116)资助

摘　　要：研究了一般平衡线性混合效应模型下的最优设计问题.主要关注模型固定效应估计,随机效应的估计以及对个体未来观察值预测的最优设计.以de la Garaz现象和Loewner偏序为工具降低求解最优设计问题的维度,用解析方法或数值方法求解最优设计,并利用等价性定理判断解的最优性.The paper investigates the problem of optimal balanced designs in general linear regression models with mixed effects. The interest lies in estimating fixed effects, random effects and prediction of the future observation of an individual, respectively. By using the de la Garaz phenomenon and Loewner order domination, the dimension of determining the optimal designs are reduced. The optimal designs are derived by using analytical or numerical methods, and their optimalities are verified through the general equivalence theorems.

关 键 词：DE LA Garza现象 Loewner偏序 混合效应模型 最优设计 

分 类 号：O212.6[理学—概率论与数理统计]