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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.

On E-Bayesian analysis of the hierarchical normal and inverse gamma model using different loss functions and its application