组内正相关的分层线性模型的A-最优设计  

A-Optimal Design for Hierarchical Linear Model with Intraclass Positive Correlation

作　　者：李凤 刘欣[1] LI Feng;LIU Xin(College of Science,Donghua University,Shanghai,201620,China)

机构地区：[1]东华大学理学院,上海201620

出　　处：《应用概率统计》2022年第4期521-530,共10页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11871143、11971318);中央高校基本科研业务费专项资金项目资助.

摘　　要：本文讨论分层线性模型的最优试验设计问题.在假定组内观测误差之间正相关条件下,分别基于群体参数的估计和个体参数的预测定义了两种A-最优准则,推导了相应的等价性定理,并通过两个例子展示了文中的结果.This paper discusses the optimal design problem for the hierarchical linear model with intraclass positive correlation.A-optimal designs are considered for the estimation of the fixed effects as well as the prediction of random effects.We provide two equivalence theorems to determine the A-optimality of a given design.Two illustrative examples of the A-optimal designs are presented.

关 键 词：A-最优设计 等价性定理 分层线性模型 正相关 

分 类 号：O212.6[理学—概率论与数理统计]