Universal admissibility of linear estimators in multivariate linear models with respect to a restricted parameter set. (Chinese. English summary) Zbl 0995.62003

Qin, Hong; Wu, Min; Peng, Junhao

Acta Math. Sci., Ser. A, Chin. Ed. 22, No. 3, 427-432 (2002).

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

Keywords:

universal admissibility; linear estimators