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Avtomat. i Telemekh., 2005, Issue 1, Pages 100–117
(Mi at1312)
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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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Automation and Remote Control, 2005, 66:1, 92–107
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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
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\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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This publication is cited in the following articles:
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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
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