Errors-in-Variables Models in Parameter Bounding

Abstract

When all observed variables of a model are affected by noise, parameter estimation is known as the errors-in-variables problem. While parameter bounding methods and algorithms have been extensively developed in the case of exactly known regressor variables, little attention has been paid to the bounded errors-in-variables problem. This chapter gives a formal proof of a previous result on the description of the feasible parameter region for models linear in the parameters in the presence of bounded errors in all variables. Topological features of the feasible parameter region, such as convexity and connectedness, are also discussed. Finally, approximate parameter uncertainty intervals are derived for ARMAX models when all the observed variables are affected by bounded noise. For an example involving extensive simulations, central estimates obtained by means of the bounded errors-in-variables approach and least squares estimates are computed and compared.