Lfinite Sample Bounds on the Performance of Weighted Linear Least Squares in Sub-Gaussian Correlated Noise

Michael Krikheli, Amir Leshem

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In this paper we provide finite sample bounds on the performance of the weighted linear least squares estimator in sub-Gaussian martingale difference correlated noise. In contrast to standard performance analysis which uses bounds on the mean square error together with asymptotic normality, our bounds are based on concentration of measure. We extend previous results by analyzing the weighted least squares estimator and provide novel results in the case of correlated noise and heteroscedasticity. Using these bounds we obtain accurate bounds on the tail of the estimator. We show fast exponential convergence of the L probability of error. We analyze the fixed design setting. We use the results to analyze the performance of the weighted least squares estimator for the important problem of system identification. We show how to extend the results to different norms and state a theorem for the L2 norm.

Original languageAmerican English
Title of host publication2019 IEEE Data Science Workshop, DSW 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages110-114
Number of pages5
ISBN (Electronic)9781728107080
DOIs
StatePublished - Jun 2019
Externally publishedYes
Event2019 IEEE Data Science Workshop, DSW 2019 - Minneapolis, United States
Duration: 2 Jun 20195 Jun 2019

Publication series

Name2019 IEEE Data Science Workshop, DSW 2019 - Proceedings

Conference

Conference2019 IEEE Data Science Workshop, DSW 2019
Country/TerritoryUnited States
CityMinneapolis
Period2/06/195/06/19

Bibliographical note

Publisher Copyright:
© 2019 IEEE.

Keywords

  • Estimation
  • concentration bounds
  • confidence bounds
  • finite sample
  • large deviations
  • martingale difference sequence
  • non Gaussian
  • system identification
  • weighted least squares

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