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}
}