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Admissibility of linear estimators of regression coefficients under quadratic loss

Admissibility of linear estimators of regression coefficients under quadratic loss For the general fixed effects linear model:Y=Xτ+ε, ε ∼N(0,V),V≥0, we obtain the necessary and sufficient conditions forLY+a to be admissible for a linear estimable functionSτ in the class of all estimators under the loss function (d -Sτ)′D(d -Sτ), whereD≥0 is known. For the general random effects linear model: $$Y = X\beta + \varepsilon ,(\begin{array}{*{20}c} \beta \\ \varepsilon \\ \end{array} ) \sim N((\begin{array}{*{20}c} {A\alpha } \\ 0 \\ \end{array} ),(\begin{array}{*{20}c} {V_{11} } & {V_{12} } \\ {V_{21} } & {V_{22} } \\ \end{array}$$ Λ=XV 11 X′+XV 12+V 21 X′+V 22≥0, we also get the necessary and sufficient conditions forLY+a to be admissible for a linear estimable functionSα+Qβ in the class of all estimators under the loss function (d -Sα -Qβ)′D(d -Sα -Qβ), whereD≥0 is known. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Admissibility of linear estimators of regression coefficients under quadratic loss

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Publisher
Springer Journals
Copyright
Copyright © 1992 by Science Press
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02014581
Publisher site
See Article on Publisher Site

Abstract

For the general fixed effects linear model:Y=Xτ+ε, ε ∼N(0,V),V≥0, we obtain the necessary and sufficient conditions forLY+a to be admissible for a linear estimable functionSτ in the class of all estimators under the loss function (d -Sτ)′D(d -Sτ), whereD≥0 is known. For the general random effects linear model: $$Y = X\beta + \varepsilon ,(\begin{array}{*{20}c} \beta \\ \varepsilon \\ \end{array} ) \sim N((\begin{array}{*{20}c} {A\alpha } \\ 0 \\ \end{array} ),(\begin{array}{*{20}c} {V_{11} } & {V_{12} } \\ {V_{21} } & {V_{22} } \\ \end{array}$$ Λ=XV 11 X′+XV 12+V 21 X′+V 22≥0, we also get the necessary and sufficient conditions forLY+a to be admissible for a linear estimable functionSα+Qβ in the class of all estimators under the loss function (d -Sα -Qβ)′D(d -Sα -Qβ), whereD≥0 is known.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Jul 15, 2005

References

  • Admissibility of Linear Estimators of Regression Coefficients in the Class of All Estimators under Matrix Loss Function
    Chen, Jianbao; Zhan, Jinlong
  • The Theory of Estimation of Parameters in Linear Model (in Chinese)
    Chen, Xiru
  • All Admissible Linear Estimates of the Mean Vector
    Cohen, A.
  • The Theory of Linear Models and Its Application (in Chinese)
    Wang, Songgui
  • Admissibility of Linear Estimators of Regression Coefficients in a General Gauss-Markov Model (in Chinese)
    Wu, Qiguang
  • Several Results on Admissibility of a Linear Estimate of Stochastic Regression Coefficients and Parameters (in Chinese)
    Wu, Qiguang
  • All Admissible Linear Estimates of Stochastic Regression Coefficients and Parameters under the Quadratic Loss Function (in Chinese)
    Wu, Qiguang
  • Characterization of Linear Admissible Estimators in Guass-Markov Model under Normality, in Linear Statistical Inference, Proceeding
    Zontek, S.