应用概率统计
應用概率統計
응용개솔통계
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS
2013年
9期
414-432
,共19页
de la Garza现象%Loewner偏序%混合效应模型%最优设计
de la Garza現象%Loewner偏序%混閤效應模型%最優設計
de la Garza현상%Loewner편서%혼합효응모형%최우설계
de la Garza phenomena%Loewner order domination%mixed effects model%optimal design
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。
研究瞭一般平衡線性混閤效應模型下的最優設計問題。主要關註模型固定效應估計，隨機效應的估計以及對箇體未來觀察值預測的最優設計。以de la Garaz現象和Loewner偏序為工具降低求解最優設計問題的維度，用解析方法或數值方法求解最優設計，併利用等價性定理判斷解的最優性。
연구료일반평형선성혼합효응모형하적최우설계문제。주요관주모형고정효응고계，수궤효응적고계이급대개체미래관찰치예측적최우설계。이de la Garaz현상화Loewner편서위공구강저구해최우설계문제적유도，용해석방법혹수치방법구해최우설계，병이용등개성정리판단해적최우성。
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.
