English

Tutorial on Asymptotic Properties of Regularized Least Squares Estimator for Finite Impulse Response Model

Statistics Theory 2022-01-03 v2 Systems and Control Systems and Control Statistics Theory

Abstract

In this paper, we give a tutorial on asymptotic properties of the Least Square (LS) and Regularized Least Squares (RLS) estimators for the finite impulse response model with filtered white noise inputs. We provide three perspectives: the almost sure convergence, the convergence in distribution and the boundedness in probability. On one hand, these properties deepen our understanding of the LS and RLS estimators. On the other hand, we can use them as tools to investigate asymptotic properties of other estimators, such as various hyper-parameter estimators.

Keywords

Cite

@article{arxiv.2112.10319,
  title  = {Tutorial on Asymptotic Properties of Regularized Least Squares Estimator for Finite Impulse Response Model},
  author = {Yue Ju and Tianshi Chen and Biqiang Mu and Lennart Ljung},
  journal= {arXiv preprint arXiv:2112.10319},
  year   = {2022}
}