平衡线性混合效应模型的最优设计

Optimal Designs for Balanced Linear Mixed-Efects Regression Models

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.