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May 2021 Finite impulse response models: A non-asymptotic analysis of the least squares estimator
Boualem Djehiche, Othmane Mazhar, Cristian R. Rojas
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Bernoulli 27(2): 976-1000 (May 2021). DOI: 10.3150/20-BEJ1262

Abstract

We consider a finite impulse response system with centered independent sub-Gaussian design covariates and noise components that are not necessarily identically distributed. We derive non-asymptotic near-optimal estimation and prediction bounds for the least squares estimator of the parameters. Our results are based on two concentration inequalities on the norm of sums of dependent covariate vectors and on the singular values of their covariance operator that are of independent value on their own and where the dependence arises from the time shift structure of the time series. These results generalize the known bounds for the independent case.

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Boualem Djehiche. Othmane Mazhar. Cristian R. Rojas. "Finite impulse response models: A non-asymptotic analysis of the least squares estimator." Bernoulli 27 (2) 976 - 1000, May 2021. https://doi.org/10.3150/20-BEJ1262

Information

Received: 1 November 2019; Revised: 1 May 2020; Published: May 2021
First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.3150/20-BEJ1262

Keywords: concentration inequality , Finite impulse response , least squares , Non-asymptotic estimation , random covariance Toeplitz matrix , shifted random vector

Rights: Copyright © 2021 ISI/BS

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Vol.27 • No. 2 • May 2021
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