李凤, 刘欣. 组内正相关的分层线性模型的A-最优设计[J]. 应用概率统计, 2022, 38(4): 521-530. DOI: 10.3969/j.issn.1001-4268.2022.04.003
引用本文: 李凤, 刘欣. 组内正相关的分层线性模型的A-最优设计[J]. 应用概率统计, 2022, 38(4): 521-530. DOI: 10.3969/j.issn.1001-4268.2022.04.003
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LI Feng, LIU Xin. A-Optimal Design for Hierarchical Linear Model with Intraclass Positive Correlation[J]. Chinese Journal of Applied Probability and Statistics, 2022, 38(4): 521-530. DOI: 10.3969/j.issn.1001-4268.2022.04.003
Citation: LI Feng, LIU Xin. A-Optimal Design for Hierarchical Linear Model with Intraclass Positive Correlation[J]. Chinese Journal of Applied Probability and Statistics, 2022, 38(4): 521-530. DOI: 10.3969/j.issn.1001-4268.2022.04.003
shu

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

    摘要
  • 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.

     

    Abstract: 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.

     

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