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Adaptive DWO Estimator of a Regression Function
INRIA, France.
Institute of Control Science, Russia.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2007 (English)Report (Other academic)
Abstract [en]

We address a problem of non-parametric estimation of an unknown regression function f : [-1/2, 1/2] → R at a fixed point x0 € (-1/2, 1/2) on the basis of observations (xi, yi), i = 1,..,n such that yi = f(xi) + ei, where ei ~ N(0, σ2) is unobservable, Gaussian i.i.d. random noise and xi € [-1/2, 1/2] are given design points. Recently, the Direct Weight Optimization (DWO) method has been proposed to solve a problem of such kind. The properties of the method have been studied for the case when the unknown function f is continuously differentiable with Lipschitz constant L. The minimax optimality and adaptivity with respect to the design have been established for the resulting estimator. However, in order to implement the approach, both L and σ are to be known. The subject of the submission is the study of an adaptive version of DWO estimator which uses a data-driven choice of the method parameter L.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2007. , 8 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2794
Keyword [en]
Non-parametric regression, Estimators, Adaptive algorithms, Mean-square error, Quadratic programming
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-56060ISRN: LiTH-ISY-R-2794OAI: oai:DiVA.org:liu-56060DiVA: diva2:316879
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-09-03Bibliographically approved

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Roll, JacobLjung, Lennart

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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  • Other style
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Language
  • de-DE
  • en-GB
  • en-US
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  • nn-NB
  • sv-SE
  • Other locale
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Output format
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