Joining models with commutative orthogonal block structure

Detalhes bibliográficos
Autor(a) principal: Santos, Carla
Data de Publicação: 2017
Outros Autores: Nunes, Célia, Dias, Cristina, Mexia, João T.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.6/9372
Resumo: Mixed linear models are a versatile and powerful tool for analysing data collected in experiments in several areas. Amixed model is a model with orthogonal block structure, OBS, when its variance–covariance matrix is ofall the positive semi-definite linear combinations of known pairwise orthogo-nal 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 Commuta-tive Jordan algebras of symmetric matrices, and the Carte-sian 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 esti-mators, 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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spelling Joining models with commutative orthogonal block structureJordan algebraMixed modelsModels with commutative orthogonal block structureModels joiningMixed linear models are a versatile and powerful tool for analysing data collected in experiments in several areas. Amixed model is a model with orthogonal block structure, OBS, when its variance–covariance matrix is ofall the positive semi-definite linear combinations of known pairwise orthogo-nal 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 Commuta-tive Jordan algebras of symmetric matrices, and the Carte-sian 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 esti-mators, 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.uBibliorumSantos, CarlaNunes, CéliaDias, CristinaMexia, João T.2020-02-19T14:46:57Z20172017-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.6/9372eng10.1016/j.laa.2016.12.019metadata only accessinfo: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:RCAAP2023-12-15T09:50:24Zoai:ubibliorum.ubi.pt:10400.6/9372Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:49:31.642794Repositório 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
Mixed models
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 T.
author_role author
author2 Nunes, Célia
Dias, Cristina
Mexia, João T.
author2_role author
author
author
dc.contributor.none.fl_str_mv uBibliorum
dc.contributor.author.fl_str_mv Santos, Carla
Nunes, Célia
Dias, Cristina
Mexia, João T.
dc.subject.por.fl_str_mv Jordan algebra
Mixed models
Models with commutative orthogonal block structure
Models joining
topic Jordan algebra
Mixed models
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. Amixed model is a model with orthogonal block structure, OBS, when its variance–covariance matrix is ofall the positive semi-definite linear combinations of known pairwise orthogo-nal 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 Commuta-tive Jordan algebras of symmetric matrices, and the Carte-sian 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 esti-mators, 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
2017-01-01T00:00:00Z
2020-02-19T14:46:57Z
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