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Teoriya Veroyatnostei i ee Primeneniya, 1974, Volume 19, Issue 2, Pages 404–409 (Mi tvp2887)  

This article is cited in 10 scientific papers (total in 10 papers)

Short Communications

On a class ol nonparametric estimates of nonlinear functionals of a density

Yu. G. Dmitriev, F. P. Tarasenko

Tomsk
Abstract: A new class of nonparametric estimated of functionals of the type $J=\int F(g(x))\,dx$ (where $F(\,\cdot\,)$ is a certain function and $g(x)$ is the unknown density function) is proposed. The estimates are based on combination of Rosenblatt–Parzen's estimate of the density and Hoeffing's $U$-statistic. They are called quasi-$U$-statistics. The performance of quasi-$U$-statistics is demonstrated by an example of estimation of the squared density integral.
Received: 15.02.1972
English version:
Theory of Probability and its Applications, 1975, Volume 19, Issue 2, Pages 390–394
DOI: https://doi.org/10.1137/1119045
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yu. G. Dmitriev, F. P. Tarasenko, “On a class ol nonparametric estimates of nonlinear functionals of a density”, Teor. Veroyatnost. i Primenen., 19:2 (1974), 404–409; Theory Probab. Appl., 19:2 (1975), 390–394
Citation in format AMSBIB
\Bibitem{DmiTar74}
\by Yu.~G.~Dmitriev, F.~P.~Tarasenko
\paper On a~class ol nonparametric estimates of nonlinear functionals of a~density
\jour Teor. Veroyatnost. i Primenen.
\yr 1974
\vol 19
\issue 2
\pages 404--409
\mathnet{http://mi.mathnet.ru/tvp2887}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=359158}
\zmath{https://zbmath.org/?q=an:0316.62013}
\transl
\jour Theory Probab. Appl.
\yr 1975
\vol 19
\issue 2
\pages 390--394
\crossref{https://doi.org/10.1137/1119045}
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  • https://www.mathnet.ru/eng/tvp/v19/i2/p404
  • This publication is cited in the following 10 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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