Teoriya Veroyatnostei i ee Primeneniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Teoriya Veroyatnostei i ee Primeneniya, 2003, Volume 48, Issue 3, Pages 534–556
DOI: https://doi.org/10.4213/tvp269
(Mi tvp269)
 

This article is cited in 28 scientific papers (total in 28 papers)

Block thresholding and sharp adaptive estimation in severely ill-posed inverse problems

L. Cavalier, Yu. F. Golubev, O. V. Lepskiĭ, A. Tsybakov

Université de Provence
References:
Abstract: We consider the problem of solving linear operator equations from noisy data under the assumptions that the singular values of the operator decrease exponentially fast and that the underlying solution is also exponentially smooth in the Fourier domain. We suggest an estimator of the solution based on a running version of block thresholding in the space of Fourier coefficients. This estimator is shown to be sharp adaptive to the unknown smoothness of the solution.
Keywords: linear operator equation, white Gaussian noise, adaptive estimation, running block thresholding.
Received: 23.07.2002
English version:
Theory of Probability and its Applications, 2004, Volume 48, Issue 3, Pages 426–446
DOI: https://doi.org/10.1137/S0040585X97980555
Bibliographic databases:
Language: English
Citation: L. Cavalier, Yu. F. Golubev, O. V. Lepskiǐ, A. Tsybakov, “Block thresholding and sharp adaptive estimation in severely ill-posed inverse problems”, Teor. Veroyatnost. i Primenen., 48:3 (2003), 534–556; Theory Probab. Appl., 48:3 (2004), 426–446
Citation in format AMSBIB
\Bibitem{CavGolLep03}
\by L.~Cavalier, Yu.~F.~Golubev, O.~V.~Lepski{\v\i}, A.~Tsybakov
\paper Block thresholding and sharp adaptive estimation in severely ill-posed inverse problems
\jour Teor. Veroyatnost. i Primenen.
\yr 2003
\vol 48
\issue 3
\pages 534--556
\mathnet{http://mi.mathnet.ru/tvp269}
\crossref{https://doi.org/10.4213/tvp269}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2141349}
\zmath{https://zbmath.org/?q=an:1130.62313}
\transl
\jour Theory Probab. Appl.
\yr 2004
\vol 48
\issue 3
\pages 426--446
\crossref{https://doi.org/10.1137/S0040585X97980555}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000224300900003}
Linking options:
  • https://www.mathnet.ru/eng/tvp269
  • https://doi.org/10.4213/tvp269
  • https://www.mathnet.ru/eng/tvp/v48/i3/p534
  • This publication is cited in the following 28 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024