A Unified Theory for Robust Bayesian Prediction Under a General Class of Regret Loss Functions

Abstract

We study robust Bayesian prediction problems using the posterior regret Γ-minimax (PRGM) approach. We provide a unified theory for PRGM prediction under a very general class of regret loss functions that includes squared error (SE), linear-exponential (LINEX), Entropy and many other loss functions as its special cases. We apply our results to the problem of predicting unknown parameters of finite populations under different superpopulation models (normal and non-normal with or without auxiliary variables) and several classes of prior distributions including the commonly used ǫ-contaminated class of priors. Results are augmented with real world applications and simulation studies.