On the Stochastic Restricted Liu Estimator under Misspecification due to Inclusion of Some Superfluous Variables

In this paper, we firstly derived the expressions of the well-known ordinary least square estimator (OLSE), the ordinary mixed estimator (OME) introduced by Theil and Golberger (1961) and the stochastic restricted Liu estimator (SRLE) proposed by Yang and Xu (2007) under misspecification due to inclusion of some superfluous variables. Then, performances of these estimators under misspecification are examined. In particular, necessary and sufficient conditions for the superiority of the SRLE over the OLSE and OME with respect to the mean squared error matrix (MSEM) criterion are derived. Furthermore, superiority of the corresponding predictors of these estimators are also investigated.