Asymptotic Theory for Regularized System Identification Part I: Empirical Bayes Hyper-Parameter Estimator

Regularized techniques, also named as kernel-based are the major advances in system identification last decade. Although many promising results have been achieved, their theoretical analysis is far from complete and there still key problems to be solved. One of them asymptotic theory, which about convergence properties model estimators sample size goes infinity. The existing related for regularized almost sure various hyper-parameter estimators. A common problem those that they do not contain information on factors affect estimators, e.g., regression matrix. In this paper, we tackle kind finite impulse response estimation with empirical Bayes (EB) estimator filtered white noise input. order expose find factors, study distribution EB estimator, its corresponding estimator. For illustration, run Monte Carlo simulations show efficacy our obtained results.