{"title":"分组比例包络模型的规模不变性和高效估算","authors":"Jing Zhang, Zhensheng Huang","doi":"10.1007/s42952-024-00277-0","DOIUrl":null,"url":null,"abstract":"<p>Motivated by different groups containing different group information under the heteroscedastic error structure, we propose the groupwise scaled envelope model that is invariable to scale changes and is permissible for distinct regression coefficients and the heteroscedastic error structure across groups. It retains the potential of the scaled envelope methods to keep the scale invariant and allows for both different regression coefficients and different error structures for diverse groups. Further, we demonstrate the maximum likelihood estimators and its theoretical properties including parameter identifiability, asymptotic distribution and consistency of the groupwise scaled envelope estimator. Lastly, simulation studies and a real-data example demonstrate the advantages of the groupwise scaled envelope estimators, including a comparison with the standard model estimators, groupwise envelope estimators, scaled envelope estimators and separate scaled envelope estimators.</p>","PeriodicalId":49992,"journal":{"name":"Journal of the Korean Statistical Society","volume":"30 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Scale invariant and efficient estimation for groupwise scaled envelope model\",\"authors\":\"Jing Zhang, Zhensheng Huang\",\"doi\":\"10.1007/s42952-024-00277-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Motivated by different groups containing different group information under the heteroscedastic error structure, we propose the groupwise scaled envelope model that is invariable to scale changes and is permissible for distinct regression coefficients and the heteroscedastic error structure across groups. It retains the potential of the scaled envelope methods to keep the scale invariant and allows for both different regression coefficients and different error structures for diverse groups. Further, we demonstrate the maximum likelihood estimators and its theoretical properties including parameter identifiability, asymptotic distribution and consistency of the groupwise scaled envelope estimator. Lastly, simulation studies and a real-data example demonstrate the advantages of the groupwise scaled envelope estimators, including a comparison with the standard model estimators, groupwise envelope estimators, scaled envelope estimators and separate scaled envelope estimators.</p>\",\"PeriodicalId\":49992,\"journal\":{\"name\":\"Journal of the Korean Statistical Society\",\"volume\":\"30 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-07-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Korean Statistical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s42952-024-00277-0\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Korean Statistical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s42952-024-00277-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Scale invariant and efficient estimation for groupwise scaled envelope model
Motivated by different groups containing different group information under the heteroscedastic error structure, we propose the groupwise scaled envelope model that is invariable to scale changes and is permissible for distinct regression coefficients and the heteroscedastic error structure across groups. It retains the potential of the scaled envelope methods to keep the scale invariant and allows for both different regression coefficients and different error structures for diverse groups. Further, we demonstrate the maximum likelihood estimators and its theoretical properties including parameter identifiability, asymptotic distribution and consistency of the groupwise scaled envelope estimator. Lastly, simulation studies and a real-data example demonstrate the advantages of the groupwise scaled envelope estimators, including a comparison with the standard model estimators, groupwise envelope estimators, scaled envelope estimators and separate scaled envelope estimators.
期刊介绍:
The Journal of the Korean Statistical Society publishes research articles that make original contributions to the theory and methodology of statistics and probability. It also welcomes papers on innovative applications of statistical methodology, as well as papers that give an overview of current topic of statistical research with judgements about promising directions for future work. The journal welcomes contributions from all countries.