Relations between Bias-Eliminating Least Squares, the Frisch scheme and Extended Compensated Least Squares methods for identifying errors-in-variables systems

There are many methods for identifying errors-in-variables systems. Among them Bias-Eliminating Least Squares (BELS), the Frisch scheme and Extended Compensated Least Squares (ECLS) methods are attractive approaches because of their simplicity and good estimation accuracy. These three methods are all based on a Bias-Compensated Least-Squares (BCLS) principle. In this paper, the relationships between them are considered. In particular, the set of nonlinear equations utilized in these three methods are proved to be equivalent under different noise conditions also for finite samples. It is shown that BELS, Frisch and ECLS methods have the same asymptotic estimation accuracy providing the same extended vector is used.