D-Optimal Designs for Hierarchical Linear Models with Heteroscedastic Errors  

作　　者：Xin Liu Rong-Xian Yue Kashinath Chatterjee 

机构地区：[1]College of Science,Donghua University,Shanghai 201620,People’s Republic of China [2]Department of Mathematics,Shanghai Normal University,Shanghai 200234,People’s Republic of China [3]Department of Statistics,Visva-Bharati University,Santiniketan,India

出　　处：《Communications in Mathematics and Statistics》2022年第4期669-679,共11页数学与统计通讯（英文）

基　　金：supported by NSFC Grant(11871143,11971318);the Fundamental Research Funds for the Central Universities;Shanghai Rising-Star Program(No.20QA1407500).

摘　　要：This paper investigates the optimal design problem for the prediction of the individual parameters in hierarchical linear models with heteroscedastic errors.An equivalence theorem is established to characterize D-optimality of designs for the prediction based on the mean squared error matrix.The admissibility of designs is also considered and a sufficient condition to simplify the design problem is obtained.The results obtained are illustrated in terms of a simple linear model with random slope and heteroscedastic errors.

关 键 词：D-optimal design HETEROSCEDASTICITY Mean squared error matrix Mixed-effect model Equivalence theorem ADMISSIBILITY 

分 类 号：O17[理学—数学]