Estimation strategies for the intercept vector in a simple linear multivariate normal regression model

Abstract

For a simple multivariate regression model, the problem of estimating the intercept vector is considered when it is apriori suspected that the slope may be restricted to a subspace. Four estimation strategies have been developed for the intercept parameter. In this situation, the estimates based on a preliminary test as well as on the Stein-rule are desirable. Exact bias and risks of all of these estimators are derived and their efficiencies relative to classical estimators are studied under quadratic loss function. An optimum rule for the preliminary test estimator is discussed. It is shown that the shrinkage estimator dominates the classical one, whereas none of the preliminary test and shrinkage estimator dominate each other. It is found that shrinkage estimator dominates the preliminary test estimator except in a range around the restriction. Further, for large values of α, the level of statistical significance, shrinkage estimator dominates the preliminary test estimator uniformly.