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Teoriya Veroyatnostei i ee Primeneniya, 1993, Volume 38, Issue 4, Pages 875–882 (Mi tvp4026)  
This article is cited in 35 scientific papers (total in 35 papers)

Short Communications

An asymptotically minimax regression estimator in the uniform norm up to exact constant

A. P. Korostelev

Institute for System Research, Russian Academy of Sciences
Full-text PDF (396 kB) Citations (35)
Abstract: We study the asymptotic behavior of the minimax risk in nonparametric regression estimation in the uniform norm in classes of functions, satisfying the Lipschitz or Holder condition. For an arbitrary loss function, the exact asymptotic behavior of the risk under equidistant observation design and Gaussian noise is found.
Keywords: nonparametric regression, minimax risk, exact asymptotic behavior, uniform norm.
Received: 30.01.1990
English version:
Theory of Probability and its Applications, 1993, Volume 38, Issue 4, Pages 737–743
DOI: https://doi.org/10.1137/1138075
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. P. Korostelev, “An asymptotically minimax regression estimator in the uniform norm up to exact constant”, Teor. Veroyatnost. i Primenen., 38:4 (1993), 875–882; Theory Probab. Appl., 38:4 (1993), 737–743
Citation in format AMSBIB
\Bibitem{Kor93}
\by A.~P.~Korostelev
\paper An asymptotically minimax regression estimator in the uniform norm up to exact constant
\jour Teor. Veroyatnost. i Primenen.
\yr 1993
\vol 38
\issue 4
\pages 875--882
\mathnet{http://mi.mathnet.ru/tvp4026}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1318004}
\zmath{https://zbmath.org/?q=an:0819.62034}
\transl
\jour Theory Probab. Appl.
\yr 1993
\vol 38
\issue 4
\pages 737--743
\crossref{https://doi.org/10.1137/1138075}
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  • https://www.mathnet.ru/eng/tvp/v38/i4/p875
    • This publication is cited in the following 35 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
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