Mean square error matrix improvements and admissibility of linear estimators

DOI10.1016/0378-3758(89)90075-XzbMath0685.62052OpenAlexW2020861206MaRDI QIDQ1262054

Erkki P. Liski, Götz Trenkler, Jerzy K. Baksalary

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0378-3758(89)90075-x

zbMATH Keywords

convexitylinear estimatorsrestricted least-squares estimatorrestricted modellinear biased estimatorsmean square error matrix criterionminimum dispersion linear unbiased estimatorsunrestricted linear regression model

Mathematics Subject Classification ID

Linear regression; mixed models (62J05) Admissibility in statistical decision theory (62C15)

Related Items (16)

Covariance adjustment in biased estimation ⋮ On partial orderings on the set of rectangular matrices ⋮ Local improvement of best linear unbiased estimation and admissibility under the weakly singular gauss-markov model ⋮ A test of the mean square error criterion for linear admissible estimators ⋮ Mean squared error matrix comparisons between biased estimators — An overview of recent results ⋮ On the \(\{2\}\)-inverse and some ordering properties of nonnegative definite matrices ⋮ Estimation From Transformed Data Under the Linear Regression Model ⋮ MSE bounds for estimators of matrix functions ⋮ Some further results on Hermitian-matrix inequalities ⋮ Proper splittings and reduced solutions of matrix equations ⋮ MSE-improvement of the least squares estimator by dropping variables ⋮ Spectrum and trace invariance criterion and its statistical applications ⋮ Characterization of admissible linear estimators in the general growth curve model with respect to an incomplete ellipsoidal restriction ⋮ MSEM dominance of estimators in two seemingly unrelated regressions ⋮ Nonnegative and positive definiteness of matrices modified by two matrices of rank one ⋮ Minimum mean square error estimation in linear regression

Cites Work

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• Ordering of nonnegative definite matrices with application to comparison of linear models
• Admissible linear estimators in restricted linear models
• Characterizations of admissible linear estimators in restricted linear models
• Correction to Estimation of parameters in a linear model
• Admissibility in linear estimation
• Mean square error matrix comparisons of estimators in linear regression
• A Test of the Mean Square Error Criterion for Restrictions in Linear Regression
• Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses
• Inequalities: theory of majorization and its applications

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