IMPROVED ESTIMATION IN A MULTIVARIATE REGRESSION-MODEL

The problem of estimating the intercept vector in a simple multivariate regression model is considered when it is a priori suspected that the slope vector may be restricted to a subspace. We propose estimators based on the outcome of the pre-test and then a shrinkage technique is employed. This estimator may be viewed as an improvement over the usual preliminary test estimator (PTE). It is important to note that the proposed estimator dominates the classical estimator over a large portion of the parameter space which is wider than that of the PTE. Furthermore, the proposed estimator is also superior in relative bias and efficiency to the usual PTE. Moreover, an optimal rule for the choice of the level of significance (alpha) for the preliminary test is presented. Table for the optimum selection of alpha is also provided for the use of the proposed estimator.