Examining the Conditions that will strengthen the Success of the Iterative Stein-Rule Estimator of The Disturbance Variance in Proxy Model

The aim of this study is to give the conditions, in a linear regression model with proxy variables, when is the difference of variances of two estimators getting closer to each other. One of the mentioned estimators is the iterative Stein-rule estimator (ISRE) of the disturbance variance which is obtained by taking the Stein-rule estimator of the parameters in the estimator of the disturbance variance; one is the usual ordinary least squares (OLS) estimator of the disturbance variance. For that purpose the theoretical difference of variances is derived and the numerical analysis is handled to see the pattern of given theoretical difference