Analysis of the prediction problem with errors in the variables

Abstract

In engineering and other scientific works, variables in a relationship are frequently measured with error, resulting in the so called erors-in-variables situation. The problem of estimating unknown parameters in the errors-in-variables model(EVM) has been extensively discussed in the literature while relatively little has been concerned with the prediction problem despite its importance in practice. In this thesis the integrated mean square error of prdiction(IMSE) is developed as a measure of the effect of the errors in the variables on the predited values 1 relationships as well as for the sum of several dependent variables from different functional relationships. The IMSE may be used for assessing the severeness of measurement errors as well as for discriminating competing estimators. This thesis is organized as follows. First, relative performances of the ordinary least squares(OLS), corrected least squares(CLS), and maximum likelihood (ML) estimation methods for the simple functional relationship are compared in terms of the IMSE in Chapter 2. Second, in chapter 3 the prediction problem for a multiple functional relationship model is defined and IMSE``s are developed for the OLS, CLS, and ML estimation methods. The analysis methods are illustrated with two examples - one for the estimation of IMSE and the other for evaluating sensitivity of IMSE to measurement errors in each independent variable. Finally, the prediction problem for the sum of dependent variables from different functional relationships is treated in Chapter 4. The corresponding IMSE``s are developed for the OLS, CLS, and ML estimation methods. An example from a standard data system in work measurement is used to illustrate how to evaluate the sensitivity of IMSE to measurement errors in each independent variable.