Bayesian estimators of the location parameter of the normal distribution with unknown variance

Abstract

The estimation of a location parameter of the normal distribution has been widely discussed and applied in various situations. The Bayes estimators under Linear Exponential (LINEX) loss are functions of the moment generating function of the Student’s t-distribution and are therefore unknown. In this paper the explicit Bayes estimators of the location parameter of the normal model for two different loss functions, the re1flected normal loss and the LINEX loss functions are proposed and evaluated. The performances of these estimators are evaluated using Monte Carlo simulation.