Orthoregressive estimates for the parameters of systems of linear difference equations

The problem of estimating the parameters of linear difference systems of equations from the observations of the segments of solutions with additive stochastic perturbations is considered. The methods of multivariate orthogonal regression are applied to obtain the estimators. The results of comparative study of the methods are exposed from the standpoint of information on linear constraints in observations. The properties of the estimators in the limit cases of a gross sample are studied. For small perturbations, a scheme for comparison of estimators by linear approximations is proposed.