An efficient, simulated and modified shrinkage procedure for the simple linear regression model

In this article, we have proposed two efficient and modified preliminary test shrunken estimators for the response of the simple linear regression model Y, and the regression parameter β when prior guess values of µY and β are available. The expressions for the bias, mean squared error, and relative efficiency of the proposed testimators are derived and studied. Numerical simulations for bias and relative efficiency show that the proposed testimators fare is better than the classical and existing shrinkage testimators. An application of real data is described; comparisons and conclusions are then given.