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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.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jul 15, 2005
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