Admissible Bayes equivariant estimation of location vectors for spherically symmetric distributions with unknown scale. (English) Zbl 1453.62284

The authors establish the admissibility of certain generalized Bayes estimators within the class of equivariant estimators, of the mean vector for a spherically symmetric distribution with unknown scale under invariants loss. In the Gaussian case, they establish admissibility within the equivariant estimators of a class of generalized Bayes minimax estimators of a particularly simple form. Similar issues in the setting of a general linear regression model with intercept and spherically symmetric error distribution are also investigated. In this setting, the shrinkage factor of equivariant estimators of the regression coefficients depends on the coefficient of determination.


62C15 Admissibility in statistical decision theory
62C20 Minimax procedures in statistical decision theory
62J05 Linear regression; mixed models
62J07 Ridge regression; shrinkage estimators (Lasso)
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