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Avtomat. i Telemekh., 2005, Issue 1, Pages 100–117 (Mi at1312)  

This article is cited in 1 scientific paper (total in 1 paper)

Adaptive and Robust Systems

Convergence of the least-squares method with a polynomial regularizer for the infinite-dimensional autoregression equation

A. E. Barabanov, Yu. R. Gel'

Saint-Petersburg State University

Abstract: Consideration was given to the estimation of the unknown parameters of a stable infinite-dimensional autoregressive model from the observations of a random time series. The class of such models includes an autoregressive moving-average equation with a stable moving-average part. A modified procedure of the least-squares method was used to identify the unknown parameters. For the infinite-dimensional case, the estimates of the least-squares method were proved to be strong consistent. In addition, presented was a fact on convergence of the semimartingales that is of independent interest.

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English version:
Automation and Remote Control, 2005, 66:1, 92–107

Bibliographic databases:

Document Type: Article
Presented by the member of Editorial Board: B. M. Miller
Received: 20.02.2003

Citation: A. E. Barabanov, Yu. R. Gel', “Convergence of the least-squares method with a polynomial regularizer for the infinite-dimensional autoregression equation”, Avtomat. i Telemekh., 2005, no. 1, 100–117; Autom. Remote Control, 66:1 (2005), 92–107

Citation in format AMSBIB
\Bibitem{BarGel05}
\by A.~E.~Barabanov, Yu.~R.~Gel'
\paper Convergence of the least-squares method with a~polynomial regularizer for the infinite-dimensional autoregression equation
\jour Avtomat. i Telemekh.
\yr 2005
\issue 1
\pages 100--117
\mathnet{http://mi.mathnet.ru/at1312}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2125955}
\zmath{https://zbmath.org/?q=an:1130.93436}
\transl
\jour Autom. Remote Control
\yr 2005
\vol 66
\issue 1
\pages 92--107
\crossref{https://doi.org/10.1007/s10513-005-0009-1}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-14844357816}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Gel Yu.R., Barabanov A., “Strong consistency of the regularized least-squares estimates of infinite autoregressive models”, J Statist Plann Inference, 137:4 (2007), 1260–1277  crossref  mathscinet  zmath  isi  elib
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