Bayes and robust Bayes predictions in a subfamily of scale parameters under a precautionary loss function. Issue 13 (2nd July 2016)

• Record Type: Journal Article
• Authors: Golparvar, Leila; Karimnezhad, Ali; Parsian, Ahmad
• Is Part Of: Communications in statistics. Volume 45:Issue 13(2016)
• Page Start: 3970
• Page End: 3992
• Publication Date: 2016-07-02
• Subjects: Bayes prediction -- Gamma distribution -- Minimax prediction -- Precautionary loss function -- Robust Bayes prediction; 62C10 -- 62F15 -- 62F35; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.915041
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: This paper deals with Bayes, robust Bayes, and minimax predictions in a subfamily of scale parameters under an asymmetric precautionary loss function. In Bayesian statistical inference, the goal is to obtain optimal rules under a specified loss function and an explicit prior distribution over the parameter space. However, in practice, we are not able to specify the prior totally or when a problem must be solved by two statisticians, they may agree on the choice of the prior but not the values of the hyperparameters. A common approach to the prior uncertainty in Bayesian analysis is to choose a class of prior distributions and compute some functional quantity. This is known as Robust Bayesian analysis which provides a way to consider the prior knowledge in terms of a class of priors Γ for global prevention against bad choices of hyperparameters. Under a scale invariant precautionary loss function, we deal with robust Bayes predictions of Y based on X . We carried out a simulation study and a real data analysis to illustrate the practical utility of the prediction procedure.