Bayes and stein estimation under asymmetric loss functions:a numerical risk comparison

We consider the estimation of the scale parameter of the shifted exponential distribution and the variance of the normal distribution when the locations of these distributions are unknown and when loss is measured by invariant asymmetric loss functions. Stein type and Bayesian estimators are derived and compared in terms of risk improvements over the best affine equivariant estimator (BAEE). It is demonstrated that, under asymmetric loss, Bayes estimators provide a much larger degree of improvement over the BAEE than Stein estimators.