Simultaneous Prediction of Actual and Average Values of Study variable Using Stein-rule

The simultaneous prediction of average and actual values of study variable in a linear regression model is considered in this paper. Generally, either of the ordinary least squares estimator or Stein-rule estimators are employed for the construction of predictors for the simultaneous prediction. A linear combination of ordinary least squares and Stein-rule predictors are utilized in this paper to construct an improved predictors. Their efficiency properties are derived using the small disturbance asymptotic theory and dominance conditions for the superiority of predictors over each other are analyzed. 1 Traditionally the predictions from a linear regression model are made either for the actual values of study variable or for the average values. However, this may not be the case in many practical situations and one may be required to predict both the actual and average values of the study variable simultaneously; see, e.g. Rao et al