Analysis of the Prediction Problem in a Simple Functional Relationship Model

Abstract

A prediction model is developed for the case where two nonstochastic variables are linearly related and both are subject to measurement errors. The performance of ordinary and grouping least-squares methods are evaluated in terms of the integrated as well as the maximum mean-square error of prediction. The proposed methodology can be used to select an appropriate estimation technique as well as assess the effect of measurement errors on the behavior of the predicted values. The results presented may also provide guidelines in designing a related experiment through a sensitivity analysis. Exact and asymptotic results are given.