Projectors and linear estimation in general linear models

DOI10.1080/03610928108828078zbMath0465.62060OpenAlexW2130937985MaRDI QIDQ3917356

Radosław Kala

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1080/03610928108828078

zbMATH Keywords

least squaresgeneral linear modelsgeneral Gauss-Markov modelminimum dispersion linear unbiased estimationtheory of projectors

Mathematics Subject Classification ID

Linear regression; mixed models (62J05) Foundations and philosophical topics in statistics (62A01) Basic linear algebra (15A99)

Related Items (11)

The general Gauss-Markov model with possibly singular dispersion matrix ⋮ Admissible linear estimation in a general Gauss-Markov model with an incorrectly specified dispersion matrix ⋮ On the notion of orthogonal projection in a semi-Euclidean space ⋮ A projector oriented approach to the best linear unbiased estimator ⋮ On nested block designs geometry ⋮ On the equality of the BLUPs under two linear mixed models ⋮ On formulae for the Moore-Penrose inverse of a columnwise partitioned matrix ⋮ Some notes on linear sufficiency ⋮ All about the \(\bot\) with its applications in the linear statistical models ⋮ Stability of invariant linearly sufficient statistics in the general Gauss-Markov model ⋮ Comparison of linear restricted models with respect to the validity of admissible and linearly sufficient estimators

Cites Work

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• General definition and decomposition of projectors and some applications to statistical problems
• A canonical form for the general linear model
• Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix
• Weak generalized inverses and minimum variance linear unbiased estimation
• On Canonical Forms, Non-Negative Covariance Matrices and Best and Simple Least Squares Linear Estimators in Linear Models
• On Best Linear Estimation and General Gauss-Markov Theorem in Linear Models with Arbitrary Nonnegative Covariance Structure
• Gauss-Markov Estimation for Multivariate Linear Models: A Coordinate Free Approach
• Comparison of Least Squares and Minimum Variance Estimates of Regression Parameters
• Linear Spaces and Minimum Variance Unbiased Estimation
• Linear Statistical Inference and its Applications

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