A Finite-Sample Deviation Bound for Stable Autoregressive Processes

2019/12/17 by Rodrigo A. González, González, Rodrigo A., Cristian R. Rojas +1 · 1 citation
Computer Science · Decision Sciences · Mathematics · #Advanced Bandit Algorithms Research #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Signal Processing (eess.SP) #Statistical Methods and Inference #Statistics Theory (math.ST) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1912.08103

openalex publication_date 2019/12/17 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28

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.

Citations

• Fundamentals of Statistical Signal Processing: Estimation Theory

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