A matrix inequality and admissibility of linear estimators with respect to the mean square error matrix criterion

DOI10.1016/0024-3795(89)90584-3zbMath0653.62009OpenAlexW2028201025MaRDI QIDQ1107916

Augustyn Markiewicz, Jerzy K. Baksalary

Publication date: 1989

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(89)90584-3

zbMATH Keywords

linear estimatorsLöwner partial orderinggeneral Gauss-Markov modelmean square error matrix

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Linear regression; mixed models (62J05) Linear inference, regression (62J99) Miscellaneous inequalities involving matrices (15A45) Admissibility in statistical decision theory (62C15)

Related Items (15)

The general Gauss-Markov model with possibly singular dispersion matrix ⋮ Matrix loss in comparison of linear experiments ⋮ The fundamental aspects of the admissibility in the quadratic approximation of linear mappings ⋮ Necessary and sufficient conditions that linear estimators of a mixed effects linear model are admissible under matrix loss function ⋮ Estimation From Transformed Data Under the Linear Regression Model ⋮ A study of the influence of the natural restrictions on estimation problems in the singular Gauss-Markov model ⋮ Admissible Estimation for Linear Combination of Fixed and Random Effects in General Mixed Linear Models ⋮ On Admissibility of Linear Estimators with Respect to the Mean Square Error Matrix Criterion Under the General Mixed Linear Model ⋮ Comparison of linear restricted models with respect to the validity of admissible and linearly sufficient estimators ⋮ Characterization of admissible linear estimators in the general growth curve model with respect to an incomplete ellipsoidal restriction ⋮ Admissible linear estimators of an arbitrary vector of parametric functions in the general Gauss-Markov model ⋮ Statistical estimation by a linear combination of two given statistics ⋮ Admissible estimators in the general multivariate linear model with respect to inequality restricted parameter set ⋮ Unnamed Item ⋮ Estimation and experiments comparison with respect to the matrix risk

Cites Work

• Correction to Estimation of parameters in a linear model
• Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix
• Categorical information and the singular linear model
• Linear Spaces and Minimum Variance Unbiased Estimation
• Inequalities: theory of majorization and its applications
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