  The aim of this paper is to develop a method to estimate high order FIR and
ARX models using least squares with re-weighted nuclear norm regularization.
Typically, the choice of the tuning parameter in the reweighting scheme is
computationally expensive, hence we propose the use of the SPARSEVA (SPARSe
Estimation based on a VAlidation criterion) framework to overcome this problem.
Furthermore, we suggest the use of the prediction error criterion (PEC) to
select the tuning parameter in the SPARSEVA algorithm. Numerical examples
demonstrate the veracity of this method which has close ties with the
traditional technique of cross validation, but using much less computations.
