Bayes, E-Bayes and robust Bayes prediction of a future observation under precautionary prediction loss functions with applications

• We introduce E-Bayesian prediction when there is a dispute over priors.
• Explicit forms of predictors in type-II censoring scheme are derived.
• We provide theoretical and numerical comparisons based on recently published works.
• We illustrate practical utility of the prediction procedure using a real data set.

In this paper we deal with Bayes, E-Bayes and robust Bayes prediction under precautionary loss functions. It is well-known that in the Bayesian framework, the Bayes rule is obtained by considering a specific prior distribution over the parameter of interest but in practice, the use of a specified prior with specific hyperparameters is critical. Specially, when a problem in the Bayesian framework is behaved by two or more statisticians, they might agree on a specific prior but not on the hyperparameter choices. To deal with such an uncertainty issue, E-Bayes and robust Bayes approaches may be called, in which some classes of priors are considered and some optimal rules are derived. In this regard, we extend the idea of E-Bayes estimation to E-Bayes prediction and as a useful alternative approach, we deal with robust Bayes prediction. We also apply these approaches to the type-II censoring scheme. We conduct a simulation study and compare performance of the Bayes, E-Bayes and robust Bayes approaches. Finally, the proposed predictors are applied to a real data analysis and reporting some existing prediction methods in the literature, we illustrate practical utility of the prediction procedures.