Robustness of Bayes Prediction Under Error-in-Variables Superpopulation Model

Abstract

In this article, we consider Bayes prediction in a finite population under the simple location error-in-variables superpopulation model. Bayes predictor of the finite population mean under Zellner's balanced loss function and the corresponding relative losses and relative savings loss are derived. The prior distribution of the unknown location parameter of the model is assumed to have a non-normal distribution belonging to the class of Edgeworth series distributions. Effects of non normality of the “true” prior distribution and that of a possible misspecification of the loss function on the Bayes predictor are illustrated for a hypothetical population.

Keywords:

• Balanced loss function
• Bayes predictor
• Edgeworth prior
• Error-in-variables model
• Kullback–Leibler distance
• Minimal Bayes predictive expected loss
• Relative loss
• Relative savings loss

Mathematics Subject Classification:

• Primary 62-02
• Secondary 62D05, 62F15, 62F35, 62P20

Acknowledgment

We are thankful to the referee for critical comments and useful suggestions.