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Properties of the matrix V + XTX' in linear statistical models

cris.virtual.author-orcid0000-0001-5473-3419
cris.virtual.author-orcid#PLACEHOLDER_PARENT_METADATA_VALUE#
cris.virtual.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.enIt is well known, due originally to C.R. Rao in early 1970s, that the best linear unbiased estimator, BLUE, of X— in the linear model M = {y, X—, V} can be expressed in the form X (XÕW≠X)≠XÕW≠y,whereW is a specific matrix of the form W = V+XTXÕ withTsatisfying the column space condition C(W)=C(X : V). Wedenote this class of matrices as W. Choice of T as an identity matrix gives an obvious member W = V + XXÕ œ W. The matrices belonging to the class W have several interesting mathematical properties. In particular, the use of matrix W œ W appears to be surprisingly handy and helpful tool when dealing with the linear statistical models. Our aim is to review and collect together some essential features of W and its use in linear statistical models. While doing this, we go through some related basic properties of the best linear unbiased estimation.
dc.affiliationWydział Rolnictwa, Ogrodnictwa i Bioinżynierii
dc.affiliation.instituteKatedra Metod Matematycznych i Statystycznych
dc.contributor.authorHaslett, Stephen J.
dc.contributor.authorMarkiewicz, Augustyn
dc.contributor.authorPuntanen, Simo
dc.date.access2026-01-12
dc.date.accessioned2026-01-12T12:17:42Z
dc.date.available2026-01-12T12:17:42Z
dc.date.copyright2022-07
dc.date.issued2022
dc.description.accesstimeat_publication
dc.description.bibliographybibliogr.
dc.description.financepublication_nocost
dc.description.financecost0,00
dc.description.number1
dc.description.points5
dc.description.versionfinal_published
dc.description.volume38
dc.identifier.issn0379-3419
dc.identifier.urihttps://sciencerep.up.poznan.pl/handle/item/6726
dc.identifier.weblinkhttps://trepo.tuni.fi/handle/10024/206036
dc.languageen
dc.relation.ispartofGujarat Journal of Statistics and Data Science
dc.relation.pages107-131
dc.rightsCC-BY
dc.sciencecloudnosend
dc.share.typeOTHER
dc.subject.enbest linear unbiased estimator
dc.subject.enBLUE
dc.subject.encolumn space
dc.subject.engeneralized inverse
dc.subject.enlöwner ordering
dc.subject.enlinear sufficiency
dc.subject.enpartitioned linear model
dc.titleProperties of the matrix V + XTX' in linear statistical models
dc.typeJournalArticle
dspace.entity.typePublication