Joining models with commutative orthogonal block structure
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://hdl.handle.net/20.500.12207/5911 |
Resumo: | Mixed linear models are a versatile and powerful tool for analysing data collected in experiments in several areas. A mixed model is a model with orthogonal block structure, OBS, when its variance–covariance matrix is of all the positive semi-definite linear combinations of known pairwise orthogonal orthogonal projection matrices that add up to the identity matrix. Models with commutative orthogonal block structure, COBS, are a special case of OBS in which the orthogonal projection matrix on the space spanned by the mean vector commutes with the variance–covariance matrix. Using the algebraic structure of COBS, based on Commutative Jordan algebras of symmetric matrices, and the Cartesian product we build up complex models from simpler ones through joining, in order to analyse together models obtained independently. This commutativity condition of COBS is a necessary and sufficient condition for the least square estimators, LSE, to be best linear unbiased estimators, BLUE, whatever the variance components. Since joining COBS we obtain new COBS, the good properties of estimators hold for the joined models. |
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Joining models with commutative orthogonal block structureJordan algebraModels with commutative orthogonal block structureModels joiningMixed linear models are a versatile and powerful tool for analysing data collected in experiments in several areas. A mixed model is a model with orthogonal block structure, OBS, when its variance–covariance matrix is of all the positive semi-definite linear combinations of known pairwise orthogonal orthogonal projection matrices that add up to the identity matrix. Models with commutative orthogonal block structure, COBS, are a special case of OBS in which the orthogonal projection matrix on the space spanned by the mean vector commutes with the variance–covariance matrix. Using the algebraic structure of COBS, based on Commutative Jordan algebras of symmetric matrices, and the Cartesian product we build up complex models from simpler ones through joining, in order to analyse together models obtained independently. This commutativity condition of COBS is a necessary and sufficient condition for the least square estimators, LSE, to be best linear unbiased estimators, BLUE, whatever the variance components. Since joining COBS we obtain new COBS, the good properties of estimators hold for the joined models.Elsevier2023-09-15T12:36:12Z2017-03-15T00:00:00Z2017-03-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.12207/5911eng0024-3795https://doi.org/10.1016/j.laa.2016.12.019Santos, CarlaNunes, CéliaDias, CristinaMexia, João Tiagoinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-09-21T09:32:00Zoai:repositorio.ipbeja.pt:20.500.12207/5911Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:29:50.904691Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Joining models with commutative orthogonal block structure |
title |
Joining models with commutative orthogonal block structure |
spellingShingle |
Joining models with commutative orthogonal block structure Santos, Carla Jordan algebra Models with commutative orthogonal block structure Models joining |
title_short |
Joining models with commutative orthogonal block structure |
title_full |
Joining models with commutative orthogonal block structure |
title_fullStr |
Joining models with commutative orthogonal block structure |
title_full_unstemmed |
Joining models with commutative orthogonal block structure |
title_sort |
Joining models with commutative orthogonal block structure |
author |
Santos, Carla |
author_facet |
Santos, Carla Nunes, Célia Dias, Cristina Mexia, João Tiago |
author_role |
author |
author2 |
Nunes, Célia Dias, Cristina Mexia, João Tiago |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Santos, Carla Nunes, Célia Dias, Cristina Mexia, João Tiago |
dc.subject.por.fl_str_mv |
Jordan algebra Models with commutative orthogonal block structure Models joining |
topic |
Jordan algebra Models with commutative orthogonal block structure Models joining |
description |
Mixed linear models are a versatile and powerful tool for analysing data collected in experiments in several areas. A mixed model is a model with orthogonal block structure, OBS, when its variance–covariance matrix is of all the positive semi-definite linear combinations of known pairwise orthogonal orthogonal projection matrices that add up to the identity matrix. Models with commutative orthogonal block structure, COBS, are a special case of OBS in which the orthogonal projection matrix on the space spanned by the mean vector commutes with the variance–covariance matrix. Using the algebraic structure of COBS, based on Commutative Jordan algebras of symmetric matrices, and the Cartesian product we build up complex models from simpler ones through joining, in order to analyse together models obtained independently. This commutativity condition of COBS is a necessary and sufficient condition for the least square estimators, LSE, to be best linear unbiased estimators, BLUE, whatever the variance components. Since joining COBS we obtain new COBS, the good properties of estimators hold for the joined models. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-03-15T00:00:00Z 2017-03-15 2023-09-15T12:36:12Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://hdl.handle.net/20.500.12207/5911 |
url |
https://hdl.handle.net/20.500.12207/5911 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0024-3795 https://doi.org/10.1016/j.laa.2016.12.019 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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