Strong consistency of ML estimators using partial fraction and elementary subsystem representation of multivariable systems

The strong consistency of ML estimators for partial fraction matrix (PFM) and elementary subsystem (ESS) representations of vector ARMA processes will be discussed for the case when the structure is overestimated. The main results of the paper are the off-line strong consistency theorems of ML estimators for PFM representation, when the number of poles is overestimated and for the ESS representations when the number of ESS's associated with the poles is overestimated.