Some remarks on a pair of seemingly unrelated regression models
Linear regression models are foundation of current statistical theory and have been a prominent object of study in statistical data analysis and inference. A special class of linear regression models is called the seemingly unrelated regression models (SURMs) which allow correlated observations betw...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2019-08-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2019-0077 |
| _version_ | 1818597811904577536 |
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| author | Hou Jian Zhao Yong |
| author_facet | Hou Jian Zhao Yong |
| author_sort | Hou Jian |
| collection | DOAJ |
| description | Linear regression models are foundation of current statistical theory and have been a prominent object of study in statistical data analysis and inference. A special class of linear regression models is called the seemingly unrelated regression models (SURMs) which allow correlated observations between different regression equations. In this article, we present a general approach to SURMs under some general assumptions, including establishing closed-form expressions of the best linear unbiased predictors (BLUPs) and the best linear unbiased estimators (BLUEs) of all unknown parameters in the models, establishing necessary and sufficient conditions for a family of equalities of the predictors and estimators under the single models and the combined model to hold. Some fundamental and valuable properties of the BLUPs and BLUEs under the SURM are also presented. |
| first_indexed | 2024-12-16T11:53:45Z |
| format | Article |
| id | doaj.art-28adc197f36543b69ff817aca7165427 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-16T11:53:45Z |
| publishDate | 2019-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-28adc197f36543b69ff817aca71654272022-12-21T22:32:37ZengDe GruyterOpen Mathematics2391-54552019-08-0117197998910.1515/math-2019-0077math-2019-0077Some remarks on a pair of seemingly unrelated regression modelsHou Jian0Zhao Yong1College of Economics and Management, Shanghai Maritime University, Shanghai, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong, ChinaLinear regression models are foundation of current statistical theory and have been a prominent object of study in statistical data analysis and inference. A special class of linear regression models is called the seemingly unrelated regression models (SURMs) which allow correlated observations between different regression equations. In this article, we present a general approach to SURMs under some general assumptions, including establishing closed-form expressions of the best linear unbiased predictors (BLUPs) and the best linear unbiased estimators (BLUEs) of all unknown parameters in the models, establishing necessary and sufficient conditions for a family of equalities of the predictors and estimators under the single models and the combined model to hold. Some fundamental and valuable properties of the BLUPs and BLUEs under the SURM are also presented.https://doi.org/10.1515/math-2019-0077surmblupbluecovariance matrixdecomposition identity62h1262j05 |
| spellingShingle | Hou Jian Zhao Yong Some remarks on a pair of seemingly unrelated regression models Open Mathematics surm blup blue covariance matrix decomposition identity 62h12 62j05 |
| title | Some remarks on a pair of seemingly unrelated regression models |
| title_full | Some remarks on a pair of seemingly unrelated regression models |
| title_fullStr | Some remarks on a pair of seemingly unrelated regression models |
| title_full_unstemmed | Some remarks on a pair of seemingly unrelated regression models |
| title_short | Some remarks on a pair of seemingly unrelated regression models |
| title_sort | some remarks on a pair of seemingly unrelated regression models |
| topic | surm blup blue covariance matrix decomposition identity 62h12 62j05 |
| url | https://doi.org/10.1515/math-2019-0077 |
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