RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
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


Teor. Veroyatnost. i Primenen., 2004, Volume 49, Issue 1, Pages 36–53 (Mi tvp235)  

This article is cited in 4 scientific papers (total in 4 papers)

A new approach to the stochastic recovery problem

B. S. Darhovsky

Institute of Systems Analysis, Russian Academy of Sciences

Abstract: We consider the problem of minimax estimation of linear functionals on function classes, also known as the recovery problem. We propose a new formalization of the original applied problem — in both deterministic and stochastic settings. For the latter case we propose a natural probability measure on the set generated by the problem's information operator. We then provides some examples of solving recovery problems in the new framework and determines the statistical properties of the stochastic recovery problem's solution. Finally, we consider an application of the proposed approach to the problem of nonparametric minimax estimation of the regression function.

Keywords: recovery problem, a posteriori distribution, nonparametric minimax estimation.

DOI: https://doi.org/10.4213/tvp235

Full text: PDF file (2047 kB)
References: PDF file   HTML file

English version:
Theory of Probability and its Applications, 2005, 49:1, 51–64

Bibliographic databases:

Received: 10.12.2001
Revised: 30.07.2002

Citation: B. S. Darhovsky, “A new approach to the stochastic recovery problem”, Teor. Veroyatnost. i Primenen., 49:1 (2004), 36–53; Theory Probab. Appl., 49:1 (2005), 51–64

Citation in format AMSBIB
\Bibitem{Dar04}
\by B.~S.~Darhovsky
\paper A new approach to the stochastic recovery problem
\jour Teor. Veroyatnost. i Primenen.
\yr 2004
\vol 49
\issue 1
\pages 36--53
\mathnet{http://mi.mathnet.ru/tvp235}
\crossref{https://doi.org/10.4213/tvp235}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2141329}
\zmath{https://zbmath.org/?q=an:1089.62042}
\transl
\jour Theory Probab. Appl.
\yr 2005
\vol 49
\issue 1
\pages 51--64
\crossref{https://doi.org/10.1137/S0040585X97980853}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000228185300003}


Linking options:
  • http://mi.mathnet.ru/eng/tvp235
  • https://doi.org/10.4213/tvp235
  • http://mi.mathnet.ru/eng/tvp/v49/i1/p36

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. S. Darhovsky, “Stochastic Recovery Problem”, Problems Inform. Transmission, 44:4 (2008), 303–314  mathnet  crossref  mathscinet  zmath  isi
    2. Darkhovsky B., “Minimax estimation of the first derivative by finite number of noisy observations”, Comm. Statist. Theory Methods, 38:16-17 (2009), 2804–2811  crossref  mathscinet  zmath  isi  elib  scopus
    3. Darkhovskiy B., “Non Asymptotic Minimax Estimation of Functionals with Noisy Observations”, Communications in Statistics-Simulation and Computation, 41:6, Part 1 Sp. Iss. SI (2012), 787–803  crossref  mathscinet  zmath  isi  scopus
    4. S. A. Bulgakov, V. M. Khametov, “Vosstanovlenie kvadratichno integriruemoi funktsii po nablyudeniyam s gaussovskimi oshibkami”, UBS, 54 (2015), 45–65  mathnet  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:245
    Full text:60
    References:68

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019