The Impact of Prior Based Loss Function for Elliptical Regression Models

In the paper we consider a multiple regression model with elliptically contoured errors. In the Bayesian view, a prior information is taken for the weight under a prior based balanced-type loss function in order to avoid making redundant assumptions. This is the essence of the Bayesian inference with vague prior information in regression analysis. It directly impacts on the performance of the quasi empirical Bayesian shrinkage estimators through the inclusion of a reciprocal weight related to the dimension of parameter space. The shrinkage factor of the estimator is also robust to outliers and the unknown density generator of elliptical models. Finally, this result is supported by an application.