D-Optimal Designs for Hierarchical Linear Models with Heteroscedastic Errors

被引：0

作者：

Liu, Xin ^{[1
]}

Yue, Rong-Xian ^{[2
]}

Chatterjee, Kashinath ^{[3
]}

机构：

[1] Donghua Univ, Coll Sci, Shanghai 201620, Peoples R China

[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[3] Visva Bharati Univ, Dept Stat, Santini Ketan, W Bengal, India

来源：

COMMUNICATIONS IN MATHEMATICS AND STATISTICS | 2022年 / 10卷 / 04期

关键词：

D-optimal design; Heteroscedasticity; Mean squared error matrix; Mixed-effect model; Equivalence theorem; Admissibility; COEFFICIENT REGRESSION-MODELS; OPTIMAL POPULATION DESIGNS; PREDICTION;

D O I：

10.1007/s40304-021-00244-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：669 / 679

页数：11

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