Two matrix-based proofs that the linear estimator \(G y\) is the best linear unbiased estimator

DOI10.1016/S0378-3758(00)00076-8zbMath0964.62054OpenAlexW1985405042MaRDI QIDQ1579993

Simo Puntanen, Hans Joachim Werner, George P. H. Styan

Publication date: 19 July 2001

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

Full work available at URL: https://doi.org/10.1016/s0378-3758(00)00076-8

zbMATH Keywords

linear modelconsistency conditionbest linear unbiased estimatorBLUEidempotent matricesGauss-Markov modelgeneralized matrix inversesquadratic unbiased estimatorsbest unbiased estimatornatural restrictionsextended BLUE approachextended estimatorstraditional BLUE approach

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Linear regression; mixed models (62J05) Matrix equations and identities (15A24) Miscellaneous inequalities involving matrices (15A45)

Related Items (14)

Some overall properties of seemingly unrelated regression models ⋮ An elementary development of the equation characterizing best linear unbiased estimators ⋮ A new approach to the concept of a strong unified-least-squares matrix ⋮ The general Gauss-Markov model with possibly singular dispersion matrix ⋮ Fundamental Equations of BLUE and BLUP in the Multivariate Linear Model with Applications ⋮ Least-norm and Extremal Ranks of the Least Square Solution to the Quaternion Matrix Equation AXB=C Subject to Two Equations ⋮ Perfect linear models and perfect parametric functions ⋮ On the best linear unbiased estimator and the linear sufficiency of a general growth curve model ⋮ The \((P,Q)\)-(skew)symmetric extremal rank solutions to a system of quaternion matrix equations ⋮ On the generalized bi (skew-) symmetric solutions of a linear matrix equation and its procrust problems ⋮ Two local operators and the BLUE ⋮ On equality of ordinary least squares estimator, best linear unbiased estimator and best linear unbiased predictor in the general linear model ⋮ The equalities of estimations under a general partitioned linear model and its stochastically restricted model ⋮ Matrix equations with restraints and their statistical applications

Cites Work

• Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix
• On inequality constrained generalized least squares selections in the general possibly singular Gauss-Markov model: A projector theoretical approach
• On Best Linear Estimation and General Gauss-Markov Theorem in Linear Models with Arbitrary Nonnegative Covariance Structure
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