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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.

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