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Universal admissibility of linear estimators in multivariate linear models with respect to a restricted parameter set. (Chinese. English summary) Zbl 0995.62003
Summary: We give some characteristics of universal admissibility for linear estimators of regression coefficients under the multivariate linear models $$(Y,X\Theta, V\otimes\Sigma)$$ and the matrix loss function $$(D(Y)-S\Theta)' (D(Y)-S\Theta)$$, where the parameters $$\Theta$$ and $$\Sigma$$ vary in the restricted class $$H_N=\{(\Theta,\Sigma)\;:\;\Theta'X'NX \Theta\leq \Sigma$$, $$N\geq 0\}$$. Our results establish the relationships between the linear admissible estimators of $$S\Theta$$ under the multivariate linear model $$(Y,X \Theta,V \otimes\Sigma)$$ and the linear admissible estimators of $$S\beta$$ under the Gauss-Markov model $$(Y,X\beta, \sigma^2V)$$ and extend some results in the literature.

##### MSC:
 62C15 Admissibility in statistical decision theory 62H12 Estimation in multivariate analysis 62F30 Parametric inference under constraints 62J05 Linear regression; mixed models