Reference points based recursive approximation

Martina Révayová; Csaba Török

Kybernetika (2013)

  • Volume: 49, Issue: 1, page 60-72
  • ISSN: 0023-5954

Abstract

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The paper studies polynomial approximation models with a new type of constraints that enable to get estimates with significant properties. Recently we enhanced a representation of polynomials based on three reference points. Here we propose a two-part cubic smoothing scheme that leverages this representation. The presence of these points in the model has several consequences. The most important one is the fact that by appropriate location of the reference points the resulting approximant of two successively assessed neighboring approximants will be smooth. We also show that the considered models provide estimates with appropriate statistical properties such as consistency and asymptotic normality.

How to cite

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Révayová, Martina, and Török, Csaba. "Reference points based recursive approximation." Kybernetika 49.1 (2013): 60-72. <http://eudml.org/doc/252511>.

@article{Révayová2013,
abstract = {The paper studies polynomial approximation models with a new type of constraints that enable to get estimates with significant properties. Recently we enhanced a representation of polynomials based on three reference points. Here we propose a two-part cubic smoothing scheme that leverages this representation. The presence of these points in the model has several consequences. The most important one is the fact that by appropriate location of the reference points the resulting approximant of two successively assessed neighboring approximants will be smooth. We also show that the considered models provide estimates with appropriate statistical properties such as consistency and asymptotic normality.},
author = {Révayová, Martina, Török, Csaba},
journal = {Kybernetika},
keywords = {approximation model; consistency; asymptotic normality; approximation model; consistency; asymptotic normality; reference points; recursive approximations},
language = {eng},
number = {1},
pages = {60-72},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Reference points based recursive approximation},
url = {http://eudml.org/doc/252511},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Révayová, Martina
AU - Török, Csaba
TI - Reference points based recursive approximation
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 1
SP - 60
EP - 72
AB - The paper studies polynomial approximation models with a new type of constraints that enable to get estimates with significant properties. Recently we enhanced a representation of polynomials based on three reference points. Here we propose a two-part cubic smoothing scheme that leverages this representation. The presence of these points in the model has several consequences. The most important one is the fact that by appropriate location of the reference points the resulting approximant of two successively assessed neighboring approximants will be smooth. We also show that the considered models provide estimates with appropriate statistical properties such as consistency and asymptotic normality.
LA - eng
KW - approximation model; consistency; asymptotic normality; approximation model; consistency; asymptotic normality; reference points; recursive approximations
UR - http://eudml.org/doc/252511
ER -

References

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