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 $\chi^2$ 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 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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