Admissibility of Bayes estimates under BLINEX loss for the normal mean problem

We consider admissibility properties of Bayes estimators in a normal mean problem derived under a parametric family of bounded asymmetric loss functions called BLINEX. We prove results on admissibility of Bayes estimators when the risk is computed under squared error loss and BLINEX loss. With noninformative prior, the Bayes estimator under squared error loss is inadmissible relative to BLINEX. Also, the Bayes estimator under BLINEX is inadmissible relative to squared error loss. These findings contrast with nondominance results obtained under conjugate prior. Our findings confirm the importance of loss structure specification, and are consistent with those obtained when the BLINEX loss is considered.