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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

, Volume 8 (3) – Jul 15, 2005
8 pages

Publisher
Springer Journals
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 SinicaSpringer Journals

Published: Jul 15, 2005

### References

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