Simple regression in view of elliptical models

Abstract

For the simple linear model Y=θ1+βx+ϵ where the error vector follows the elliptically contoured distribution, we consider the unrestricted, restricted, preliminary test and shrinkage estimators for the intercept parameter, θ when it is suspected that the slope parameter β may be βo. The exact bias and MSE expressions are derived and the mean-square relative efficiency is taken to determine the relative dominance properties of the proposed estimators in comparison. In the continuation, the optimal level of significance of the preliminary test estimator is tabulated and some graphical result are also displayed.