{"title":"线性混合模型及其变换模型中blp相等关系的秩法","authors":"Melek Eriş Büyükkaya, Nesrin Güler, Melike Yigit","doi":"10.33401/FUJMA.889229","DOIUrl":null,"url":null,"abstract":"A linear mixed model (LMM) M : y = Xβ +Zu+ ε with general assumptions and its transformed model T : Ty = TXβ +TZu+Tε are considered. This work concerns the comparison problem of predictors under M and T . Our aim is to establish equality relations between the best linear unbiased predictors (BLUPs) of unknown vectors under two LMMs M and T through their covariance matrices by using various rank formulas of block matrices and elementary matrix operations.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model\",\"authors\":\"Melek Eriş Büyükkaya, Nesrin Güler, Melike Yigit\",\"doi\":\"10.33401/FUJMA.889229\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A linear mixed model (LMM) M : y = Xβ +Zu+ ε with general assumptions and its transformed model T : Ty = TXβ +TZu+Tε are considered. This work concerns the comparison problem of predictors under M and T . Our aim is to establish equality relations between the best linear unbiased predictors (BLUPs) of unknown vectors under two LMMs M and T through their covariance matrices by using various rank formulas of block matrices and elementary matrix operations.\",\"PeriodicalId\":199091,\"journal\":{\"name\":\"Fundamental Journal of Mathematics and Applications\",\"volume\":\"2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fundamental Journal of Mathematics and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33401/FUJMA.889229\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamental Journal of Mathematics and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33401/FUJMA.889229","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
考虑了具有一般假设条件的线性混合模型M: y = Xβ +Zu+ ε及其变换后的模型T: Ty = TXβ +TZu+ ε。本文研究了M和T条件下预测因子的比较问题。我们的目的是利用分块矩阵的各种秩公式和初等矩阵运算，通过协方差矩阵建立两个lmm M和T下未知向量的最佳线性无偏预测量(blps)之间的相等关系。
Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model
A linear mixed model (LMM) M : y = Xβ +Zu+ ε with general assumptions and its transformed model T : Ty = TXβ +TZu+Tε are considered. This work concerns the comparison problem of predictors under M and T . Our aim is to establish equality relations between the best linear unbiased predictors (BLUPs) of unknown vectors under two LMMs M and T through their covariance matrices by using various rank formulas of block matrices and elementary matrix operations.
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