Admissibility of generalized Bayes estimators in linear regression with hierarchical g‐priors

We study the admissibility of generalized Bayes estimators for regression coefficients in normal linear models under hierarchical ‐priors. While admissibility results are available for canonical normal means problems with unknown variance, their applicability to the regression problem is nontrivial. We explore the admissibility of regression‐induced generalized Bayes estimators under scaled quadratic loss with arbitrary positive definite weight matrices by carefully transporting recent normal means results to the regression parameter. Explicit conditions on the hyperparameters governing the prior on are derived. Our results provide a decision‐theoretic justification for generalized Bayes estimators of regression coefficients under hierarchical g‐priors.