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

共 50 条

[21] D-optimal designs for Poisson regression models
Wang, Yanping
Myers, Raymond H.
Smith, Eric. P.
Ye, Keying
[J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2006, 136 (08) : 2831 - 2845
[22] D-Optimal designs for quadratic regression models
van Berkum, EEM
Pauwels, B
Upperman, PM
[J]. ADVANCES IN STOCHASTIC SIMULATION METHODS, 2000, : 189 - 195
[23] D-OPTIMAL DESIGNS FOR POISSON REGRESSION MODELS
Russell, K. G.
Woods, D. C.
Lewis, S. M.
Eccleston, J. A.
[J]. STATISTICA SINICA, 2009, 19 (02) : 721 - 730
[24] D-OPTIMAL DESIGNS FOR MULTINOMIAL LOGISTIC MODELS
Bu, Xianwei
Majumdar, Dibyen
Yang, Jie
[J]. ANNALS OF STATISTICS, 2020, 48 (02): : 983 - 1000
[25] D-optimal designs for multi-response linear models with two groups
Liu, Xin
He, Lei
Yue, Rong-Xian
[J]. STAT, 2024, 13 (01):
[26] Linear models and D-optimal designs for n equivalent to 2 mod 4
Koukouvinos, C
[J]. STATISTICS & PROBABILITY LETTERS, 1996, 26 (04) : 329 - 332
[27] D-OPTIMAL DESIGNS FOR PARTIALLY NON-LINEAR REGRESSION-MODELS
HILL, PDH
[J]. TECHNOMETRICS, 1980, 22 (02) : 275 - 276
[28] Bayesian D-optimal designs for generalized linear models with a varying dispersion parameter
Pinto, ER
de Leon, AP
[J]. MODA 7 - ADVANCES IN MODEL-ORIENTED DESIGN AND ANALYSIS, PROCEEDINGS, 2004, : 143 - 151
[29] Analytic solutions for D-optimal factorial designs under generalized linear models
Tong, Liping
Volkmer, Hans W.
Yang, Jie
[J]. ELECTRONIC JOURNAL OF STATISTICS, 2014, 8 : 1322 - 1344
[30] BAYESIAN D-OPTIMAL AND MODEL ROBUST DESIGNS IN LINEAR-REGRESSION MODELS
DETTE, H
[J]. STATISTICS, 1993, 25 (01) : 27 - 46

← 1 2 3 4 5 →