Fundamental Equations of BLUE and BLUP in the Multivariate Linear Model with Applications

DOI10.1080/03610926.2011.585007zbMath1298.62126OpenAlexW2018489814MaRDI QIDQ5299084

Chenqi Xia, Yong Hui Liu

Publication date: 25 June 2013

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

Full work available at URL: https://doi.org/10.1080/03610926.2011.585007

zbMATH Keywords

projection methodBLUPBLUEmultivariate linear modelOLSEmatrix rank methodlinear BLUE-sufficiencylinear BLUP-sufficiencyvectorization method

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Generalized linear models (logistic models) (62J12)

Related Items (1)

On simultaneous prediction in a multivariate general linear model with future observations

Cites Work

• On the equivalence of estimations under a general linear model and its transformed models
• Linear sufficiency and admissibility in restricted linear models
• Linear transformations preserving best linear unbiased estimators in a general Gauss-Markoff model
• An extension of a rank criterion for the least squares estimator to be the best linear unbiased estimator
• Comparison of linear restricted models with respect to the validity of admissible and linearly sufficient estimators
• Least squares in general vector spaces revisited.
• Two matrix-based proofs that the linear estimator \(G y\) is the best linear unbiased estimator
• Linear sufficiency with respect to a given vector of parametric functions
• Sufficiency and completeness in the linear model
• On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model
• Sufficient and admissible estimators in general multivariate linear model
• More on extremal ranks of the matrix expressions A  − BX  ± X ^* B ^* with statistical applications
• Fixed rank solutions of the matrix equation with statistical applications
• On Sum Decompositions of Weighted Least-Squares Estimators for the Partitioned Linear Model
• Linear Prediction Sufficiency for New Observations in the General Gauss–Markov Model
• Prediction and the efficiency of least squares

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