On equality of ordinary least squares estimator, best linear unbiased estimator and best linear unbiased predictor in the general linear model

DOI10.1016/j.jspi.2008.08.015zbMath1153.62334OpenAlexW1972082064MaRDI QIDQ999009

Yong Hui Liu

Publication date: 30 January 2009

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jspi.2008.08.015

zbMATH Keywords

best linear unbiased estimator (BLUE)best linear unbiased predictor (BLUP)general linear modelmatrix rank methodordinary least squares estimator (OLSE)

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Linear regression; mixed models (62J05) Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24)

Related Items (7)

The minimal rank of \(A - BX\) with respect to Hermitian matrix ⋮ On relations between BLUPs under two transformed linear random-effects models ⋮ The minimal rank of matrix expressions with respect to Hermitian matrix-revised ⋮ On the equality of estimators under a general partitioned linear model with parameter restrictions ⋮ Equalities between OLSE, BLUE and BLUP in the linear model ⋮ Ranks of Hermitian and skew-Hermitian solutions to the matrix equation \(AXA^*=B\) ⋮ The Equalities of BLUPs for Linear Combinations Under Two General Linear Mixed Models

Cites Work

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• Simple least squares estimation versus best linear unbiased prediction
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• On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model
• More on extremal ranks of the matrix expressions A  − BX  ± X ^* B ^* with statistical applications
• Best Linear Unbiased Prediction in the Generalized Linear Regression Model
• Linear Prediction Sufficiency for New Observations in the General Gauss–Markov Model
• Prediction and the efficiency of least squares

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