On Sum Decompositions of Weighted Least-Squares Estimators for the Partitioned Linear Model

DOI10.1080/03610920701648862zbMath1139.62029OpenAlexW2057849332MaRDI QIDQ5450535

Yoshio Takane, Yongge Tian

Publication date: 12 March 2008

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610920701648862

zbMATH Keywords

Moore-Penrose inverseprojectormatrix rank methodWLSEsum decompositionssmall models

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Linear regression; mixed models (62J05)

Related Items (17)

Some overall properties of seemingly unrelated regression models ⋮ On decompositions of BLUEs under a partitioned linear model with restrictions ⋮ Fundamental Equations of BLUE and BLUP in the Multivariate Linear Model with Applications ⋮ On relations between weighted least-squares estimators of parametric functions under a general partitioned linear model and its small models ⋮ On equalities for BLUEs under misspecified Gauss-Markov models ⋮ Estimations of parametric functions under a system of linear regression equations with correlated errors ⋮ On additive decompositions of solutions of the matrix equation \(AXB=C\) ⋮ On decompositions of estimators under a general linear model with partial parameter restrictions ⋮ Some equalities for estimations of partial coefficients under a general linear regression model ⋮ The additive and block decompositions about the WLSEs of parametric functions for a multiple partitioned linear regression model ⋮ On additive and block decompositions of WLSEs under a multiple partitioned regression model ⋮ Equalities for orthogonal projectors and their operations ⋮ On \(\mathbf V\)-orthogonal projectors associated with a semi-norm ⋮ On an additive decomposition of the BLUE in a multiple-partitioned linear model ⋮ Approximation and continuity of Moore-Penrose inverses of orthogonal row block matrices ⋮ On the equivalence of estimations under a general linear model and its transformed models ⋮ Ranks of Hermitian and skew-Hermitian solutions to the matrix equation \(AXA^*=B\)

Cites Work

• Unnamed Item
• Unnamed Item
• Predictor-corrector smoothing methods for monotone LCP
• Projections under seminorms and generalized Moore Penrose inverses
• On a partitioned linear model and some associated reduced models
• Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix
• Estimation under a general partitioned linear model
• The maximal and minimal ranks of some expressions of generalized inverses of matrices
• A BLUE decomposition in the general linear regression model
• On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model
• A property of partitioned generalized regression
• PARTIALLY SUPERFLUOUS OBSERVATIONS
• THREE RANK FORMULAS ASSOCIATED WITH THE COVARIANCE MATRICES OF THE BLUE AND THE OLSE IN THE GENERAL LINEAR MODEL

This page was built for publication: On Sum Decompositions of Weighted Least-Squares Estimators for the Partitioned Linear Model