D-optimal Designs for Multiresponse Linear Models with a Qualitative Factor Under General Covariance Structure

作     者：Rong-Xian YUE Xin LIU Kashinath CHATTERJEE Rong-Xian YUE;Xin LIU;Kashinath CHATTERJEE

作者机构：College of Mathematics and ScienceShanghai Normal UniversityShanghai 200234China College of ScienceDonghua UniversityShanghai 201620China Department of StatisticsVisva-Bharati UniversitySantiniketanIndia 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2023年第39卷第4期

页      面：878-885页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China (Nos.11971318, 11871143) the Fundamental Research Funds for the Central Universities (No.2232020D-38) 

主　　题：D-optimal designs Multiresponse linear models Qualitative factors 

摘      要：This paper considers a linear regression model involving both quantitative and qualitative factors and an m-dimensional response variable y. The main purpose of this paper is to investigate D-optimal designs when the levels of the qualitative factors interact with the levels of the quantitative factors. Under a general covariance structure of the response vector y, here we establish that the determinant of the information matrix of a product design can be separated into two parts corresponding to the two marginal designs. Moreover, it is also proved that D-optimal designs do not depend on the covariance structure if we assume hierarchically ordered system of regression models.