Simple item page
 

The Fundamental BLUE Equation in Linear Models Revisited

cris.virtual.author-orcid#PLACEHOLDER_PARENT_METADATA_VALUE#
cris.virtual.author-orcid#PLACEHOLDER_PARENT_METADATA_VALUE#
cris.virtual.author-orcid#PLACEHOLDER_PARENT_METADATA_VALUE#
cris.virtual.author-orcid#PLACEHOLDER_PARENT_METADATA_VALUE#
cris.virtualsource.author-orcid#PLACEHOLDER_PARENT_METADATA_VALUE#
cris.virtualsource.author-orcide9e0b41e-e4f0-4842-94d4-95738eaea207
cris.virtualsource.author-orcid#PLACEHOLDER_PARENT_METADATA_VALUE#
cris.virtualsource.author-orcid#PLACEHOLDER_PARENT_METADATA_VALUE#
dc.abstract.enIn the world of linear statistical models there is a particular matrix equation, G(X :VX⊥) =(X:0), which is sufficiently important that it is sometimes called the fundamental BLUE equation. In this equation, X is a model matrix, V is the covariance matrix of y in the linear model y = Xβ+ε, and we are interested in finding the best linear estimator, BLUE, of Xβ. Any solution G for this equation has the property that Gy provides a representation for the BLUE of Xβ: this is the message of the the fundamental BLUE equation, whose main developer was the late Professor C. R. Rao in early 1970s. In this article we revisit some interesting features and consequences of this equation. We do not provide essentially new results– the aim is to offer a compact easy-to-follow review including also some recent related results by the authors.
dc.affiliationWydział Rolnictwa, Ogrodnictwa i Biotechnologii
dc.affiliation.instituteKatedra Metod Matematycznych i Statystycznych
dc.contributor.authorHaslett, Stephen J.
dc.contributor.authorIsotalo, Jarkko
dc.contributor.authorMarkiewicz, Augustyn
dc.contributor.authorPuntanen, Simo
dc.date.access2025-08-21
dc.date.accessioned2025-03-27T12:34:05Z
dc.date.available2025-03-27T12:34:05Z
dc.date.copyright2024-06-09
dc.date.issued2024
dc.description.accesstimeat_publication
dc.description.bibliographybibliogr.
dc.description.financepublication_nocost
dc.description.financecost0,00
dc.description.if0,4
dc.description.number3
dc.description.points20
dc.description.versionfinal_published
dc.description.volume22
dc.identifier.eissn2454-7395
dc.identifier.issn2454-7395
dc.identifier.urihttps://sciencerep.up.poznan.pl/handle/item/2636
dc.identifier.weblinkhttps://ssca.org.in/journalvolumes/1/
dc.languageen
dc.relation.ispartofStatistics and Applications
dc.relation.pages95-118
dc.rightsOther
dc.sciencecloudnosend
dc.share.typeOPEN_JOURNAL
dc.subject.enBLUE
dc.subject.enBLUP
dc.subject.encovariance matrix
dc.subject.enequality of the BLUEs
dc.subject.enlinear sufficiency
dc.subject.enmisspecified model
dc.titleThe Fundamental BLUE Equation in Linear Models Revisited
dc.typeJournalArticle
dspace.entity.typePublication