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

  • Adaptive and Robust Systems
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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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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    A. E. Barabanov & Yu. R. Gel’

Authors
  1. A. E. Barabanov
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  2. Yu. R. Gel’
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Additional information

This work was supported in part by the Russian Foundation for Basic Research, projects nos. 01-01-00306, 04-01-00084, and project no. 00-15-96-028 for the Russian Scientific Schools.

Translated from Avtomatika i Telemekhanika, No. 1, 2005, pp. 100–117.

Original Russian Text Copyright © 2005 by Barabanov, Gel’.

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Barabanov, A.E., Gel’, Y.R. Convergence of the least-squares method with a polynomial regularizer for the infinite-dimensional autoregression equation. Autom Remote Control 66, 92–107 (2005). https://doi.org/10.1007/s10513-005-0009-1

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  • DOI: https://doi.org/10.1007/s10513-005-0009-1

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