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Title: Biadditive models: Commutativity and optimum estimators
Authors: Coholina, Armando Alexandre
Oliveira, Manuela
Garção, Eugénio Garção
Mexia, João
Keywords: Bi-additive models
optimum estimators
Issue Date: 2022
Publisher: Communications in Statistics - Theory and Methods
Citation: Armando Alexandre, Manuela Oliveira, Eugénio Garção & João Mexia (2022) Biadditive models: Commutativity and optimum estimators, Communications in Statistics - Theory and Methods, DOI: 10.1080/03610926.2022.2117560
Abstract: Bi-additive models, are given by the sum of a fixed effects term Xβ and w independent random terms X1Z1,…, XwZw, the components of Z1,…,Zw being independent and identically distributed (i.i.d.) with null mean values and variances σ21,…,σ2w. Thus besides having an additive structure they have covariance matrix ∑wi=1σ2iMi, with Mi=XiXti,i=1,…,w, thus their name. When matrices M1,…,Mw, commute the covariance matrix will be a linear combination ∑mj=1γjQj of known, pairwise orthogonal, orthogonal projection matrices and we obtain BQUE for the γ1,…,γm through an extension of the HSU theorem and, when these matrices also commute with M=XXt, we also derive BLUE for γ. The case in which the Z1,…,Zw are normal is singled out and we then also obtain BQUE for the σ21,…,σ2w. The interest of these models is that the types of the distributions of the components of vectors Z1,…,Zw may belong to a wide family. This enlarges the applications of mixed models which has been centered on the normal type.
Type: article
Appears in Collections:DEM - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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