Robust Bayesian prediction under a general linear-exponential posterior risk function and its application in finite population

Razieh Jafaraghaie and Nader Nematollahi

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 13, 3269-3292

Abstract: We consider robust Bayesian prediction of a function of unobserved data based on observed data under an asymmetric loss function. Under a general linear-exponential posterior risk function, the posterior regret gamma-minimax (PRGM), conditional gamma-minimax (CGM), and most stable (MS) predictors are obtained when the prior distribution belongs to a general class of prior distributions. We use this general form to find the PRGM, CGM, and MS predictors of a general linear combination of the finite population values under LINEX loss function on the basis of two classes of priors in a normal model. Also, under the general ε-contamination class of prior distributions, the PRGM predictor of a general linear combination of the finite population values is obtained. Finally, we provide a real-life example to predict a finite population mean and compare the estimated risk and risk bias of the obtained predictors under the LINEX loss function by a simulation study.

Date: 2018
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DOI: 10.1080/03610926.2017.1383425

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