Improvement of the Liu estimator in linear regression model

In the presence of stochastic prior information, in addition to the sample, Theil and Goldberger (1961) introduced a Mixed Estimator (beta) over cap (m) for the parameter vector beta in the standard multiple linear regression model (Y,X beta,sigma I-2). Recently, the Liu estimator which is an alternative biased estimator for beta has been proposed by Liu (1993). In this paper we introduce another new Liu type biased estimator called Stochastic restricted Liu estimator (beta) over cap (srd) for beta, and discuss its efficiency. The necessary and sufficient conditions for mean squared error matrix of the Stochastic restricted Liu estimator A. to exceed the mean squared error matrix of the mixed estimator (beta) over cap (m) will be derived for the two cases in which the parametric restrictions are correct and are not correct In particular we show that this new biased estimator is superior in the mean squared error matrix sense to both the Mixed estimator (beta) over cap (m) and to the biased estimator introduced by Liu (1993).