A Finite-Sample Deviation Bound for Stable Autoregressive Processes
Abstract
In this paper, we study non-asymptotic deviation bounds of the least squares estimator in Gaussian AR($n$) processes. By relying on martingale concentration inequalities and a tail-bound for $\chi^2$ distributed variables, we provide a concentration bound for the sample covariance matrix of the process output. With this, we present a problem-dependent finite-time bound on the deviation probability of any fixed linear combination of the estimated parameters of the AR$(n)$ process. We discuss extensions and limitations of our approach.
Cite
Text
González and Rojas. "A Finite-Sample Deviation Bound for Stable Autoregressive Processes." Proceedings of the 2nd Conference on Learning for Dynamics and Control, 2020.Markdown
[González and Rojas. "A Finite-Sample Deviation Bound for Stable Autoregressive Processes." Proceedings of the 2nd Conference on Learning for Dynamics and Control, 2020.](https://mlanthology.org/l4dc/2020/gonzalez2020l4dc-finitesample/)BibTeX
@inproceedings{gonzalez2020l4dc-finitesample,
title = {{A Finite-Sample Deviation Bound for Stable Autoregressive Processes}},
author = {González, Rodrigo A. and Rojas, Cristian R.},
booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control},
year = {2020},
pages = {191-200},
volume = {120},
url = {https://mlanthology.org/l4dc/2020/gonzalez2020l4dc-finitesample/}
}