On E-Bayesian Analysis of the Hierarchical Normal and Inverse Gamma Model Using Different Loss Functions and Its Application

This paper introduces the idea of hierarchical modelling to derive the variance (i.e. squared scale) parameter of the hierarchical normal and inverse gamma model using E-Bayesian estimation. We propose the idea of a hierarchical probability density function instead of the traditional hierarchical prior density function. We aim to derive E-Bayesian estimators with respect to the conjugate prior distribution IG(a,b) on the basis of the Balanced squared error loss function (BSELF) and Stein's loss function (STLF) for the unknown squared scale parameter. We use E-Posterior Risk as an evaluation standard. This study also intends to reveal the relationship among the E-Bayesian estimates under three distinct bivariate independent prior distributions of hyperparameters. The asymptotic properties of the E-Bayesian estimators are also evaluated. Monte Carlo simulations are prosecuted to study the efficiency of E-Bayesian estimators empirically and also, a real data application is analysed for exemplifying purposes.