On the Bayesianity of minimum risk equivariant estimator for location or scale parameters under a general convex and invariant loss function

The Minimum Risk Equivariant (MRE), estimator is a widely used estimator which has several well-known theoretical and practical properties. It is well known that for the square error and absolute error loss functions, the MRE estimator is a generalized Bayes estimator. This article investigates the potential Bayesianity (or generalized Bayesianity) of the MRE estimator under a general convex and invariant loss function, ρ(·), for estimating the location and scale parameters of an unimodal density function.