Analysis of the Prediction Problem with Errors in the Variables

Abstract

In engineering and other scientific works variables are frequently measured with error, resulting in so-called errors-in-variables situations. The problem of estimating unknown parameters in an errors-in-variables model (EVM)has been extensively discussed in the literature while relatively little has been concerned with the prediction problem in the EVM context. In this paper the integrated mean square, error of prediction (TMSE) is developed for a multiple functional relationship model as a measure of the effect of errors in the variables on the predicted values. The IMSE may be used for assessing the severeness of measurement errors as well as for discriminating competing estimators. Relative performances of various estimation methods for a simple functional relationship are compared in terms of the IMSB, Proposed methods are illustrated with two examples, one from business forecasting and the other from work measurement.