A Generalization of Least Squares Estimation

It is well known that the (naive) least squares approach to the estimation problem in functional relationships leads to inconsistent results if the information matrix is not known exactly. In this paper an estimation method, denoted by “Least-Squares-Like”, is developed. This method can be used if two sets of observations of the explaining variables, both containing disturbances, are available. Its statistical properties are derived. The method is discussed from the point of view of system parameter estimation using input and output measurements contaminated by noise. The properties of this estimator are compared to those of the maximum likelihood one. The instrumental variable method can be considered as a special case of this least-squares-like approach.