A Finite-Sample Deviation Bound for Stable Autoregressive Processes

Rodrigo A. González, Cristian R. Rojas
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:191-200, 2020.

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 χ2 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 this Paper

BibTeX
@InProceedings{pmlr-v120-gonzalez20a, title = {A Finite-Sample Deviation Bound for Stable Autoregressive Processes}, author = {Gonz\'alez, Rodrigo A. and Rojas, Cristian R.}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {191--200}, year = {2020}, editor = {Bayen, Alexandre M. and Jadbabaie, Ali and Pappas, George and Parrilo, Pablo A. and Recht, Benjamin and Tomlin, Claire and Zeilinger, Melanie}, volume = {120}, series = {Proceedings of Machine Learning Research}, month = {10--11 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v120/gonzalez20a/gonzalez20a.pdf}, url = {https://proceedings.mlr.press/v120/gonzalez20a.html}, 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. } }
Endnote
%0 Conference Paper %T A Finite-Sample Deviation Bound for Stable Autoregressive Processes %A Rodrigo A. González %A Cristian R. Rojas %B Proceedings of the 2nd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2020 %E Alexandre M. Bayen %E Ali Jadbabaie %E George Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire Tomlin %E Melanie Zeilinger %F pmlr-v120-gonzalez20a %I PMLR %P 191--200 %U https://proceedings.mlr.press/v120/gonzalez20a.html %V 120 %X 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.
APA
González, R.A. & Rojas, C.R.. (2020). A Finite-Sample Deviation Bound for Stable Autoregressive Processes. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:191-200 Available from https://proceedings.mlr.press/v120/gonzalez20a.html.

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