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Cybernetics and Systems Analysis

, Volume 47, Issue 1, pp 85–94 | Cite as

Estimating functional dependences based on time series with the use of classes of regression functions of infinite capacity

  • N. D. Pankratova
  • A. G. Zrazhevsky
Article
  • 29 Downloads

Abstract

The problem of estimating the functional dependence of time series on the time index is considered in the case of short data samples. It is proved that empirical risk functional uniformly converges to the theoretical one in the case where regression functions can be approximated by finite-degree polynomials. An example of estimating the functional dependence for a class of trigonometric functions is presented.

Keywords

time series estimation of functional dependences uniform convergence polynomial approximation 

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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Institute of Applied Systems Analysis, National Technical University “Kyiv Polytechnic Institute,”National Academy of Sciences of Ukraine and Ministry of Education and Science of UkraineKyivUkraine

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