Robust Bayesian prediction and estimation under a squared log error loss function

Robust Bayesian analysis is concerned with the problem of making decisions about some future observation or an unknown parameter, when the prior distribution belongs to a class ΓΓ instead of being specified exactly. In this paper, the problem of robust Bayesian prediction and estimation under a squared log error loss function is considered. We find the posterior regret ΓΓ-minimax predictor and estimator in a general class of distributions. Furthermore, we construct the conditional ΓΓ-minimax, most stable and least sensitive prediction and estimation in a gamma model. A prequential analysis is carried out by using a simulation study to compare these predictors.