Average mean square error of prediction for a multiple functional relationship model

Abstract

In a linear regression model the independent variables are frequently subject to measurement errors. For this case, the problem of estimating unknown parameters has been extensively discussed in the literature while very few has been concerned with the effect of measurement errors on prediction. This paper investigates the behavior of the predicted values of the dependent variable in terms of the average mean square error of prediction(AMSEP). AMSEP may be used as a criterion for selecting an appropriate estimation method, for designing an estimation experiment, and for developing cost-effective future sampling schemes.