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

Nader Nematollahi, Mohammad Jafari Jozani, Razieh Jafaraghaie

2021

Statistica Sinica

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 the squared error, linearexponential, entropy and many other loss functions as special cases. We apply our results to the problem of predicting unknown parameters for 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 e-contaminated class of priors. Our results are augmented with real-world applications and simulation studies.