{"title":"一般协方差结构下具有定性因子的多响应线性模型的D最优设计","authors":"Rong-Xian Yue, Xin Liu, Kashinath Chatterjee","doi":"10.1007/s10255-023-1089-9","DOIUrl":null,"url":null,"abstract":"<div><p>This paper considers a linear regression model involving both quantitative and qualitative factors and an <i>m</i>-dimensional response variable <b><i>y</i></b>. The main purpose of this paper is to investigate <i>D</i>-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 <b><i>y</i></b>, 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 <i>D</i>-optimal designs do not depend on the covariance structure if we assume hierarchically ordered system of regression models.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"39 4","pages":"878 - 885"},"PeriodicalIF":0.9000,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"D-optimal Designs for Multiresponse Linear Models with a Qualitative Factor Under General Covariance Structure\",\"authors\":\"Rong-Xian Yue, Xin Liu, Kashinath Chatterjee\",\"doi\":\"10.1007/s10255-023-1089-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper considers a linear regression model involving both quantitative and qualitative factors and an <i>m</i>-dimensional response variable <b><i>y</i></b>. The main purpose of this paper is to investigate <i>D</i>-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 <b><i>y</i></b>, 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 <i>D</i>-optimal designs do not depend on the covariance structure if we assume hierarchically ordered system of regression models.</p></div>\",\"PeriodicalId\":6951,\"journal\":{\"name\":\"Acta Mathematicae Applicatae Sinica, English Series\",\"volume\":\"39 4\",\"pages\":\"878 - 885\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-11-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematicae Applicatae Sinica, English Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10255-023-1089-9\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematicae Applicatae Sinica, English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10255-023-1089-9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
D-optimal Designs for Multiresponse Linear Models with a Qualitative Factor Under General Covariance Structure
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.
期刊介绍:
Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.