ESTIMATION OF PARAMETERS OF THE SIMPLE MULTIVARIATE LINEAR MODEL WITH STUDENT-t ERRORS

This paper considers estimation of the intercept and slope vector parameters of the simple multivariate linear regression model with Student-t errors in the presence of uncertain prior information on the value of the unknown slope vector. The unrestricted, restricted, preliminary test, shrinkage, and positive-rule shrinkage estimators are defined together with the expressions for the bias, quadratic bias, quadratic risk and mean squared errors (mse) functions of the estimators are derived. Comparison of the estimators is made using quadratic risk criterion. Based on the study we conclude that for p ≥ 3 shrinkage estimators are recommended, and for p ≤ 2, the preliminary test estimators are preferable.