Prediction Problem for Random Vector

This article deals with the problem of finding the set predictor for a random vector where the choice of sets considered is restricted to a class of se ts which arc linear translates of a symmetric convex set. The loss function considered is a linear functi on of some measure of the size of the set and the distance of the set from the actual observed value. The prediction distribution considered is also symmetric. The result s are directly applicable to solve the correspoading Bayesian estimation problem,