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Teoriya Veroyatnostei i ee Primeneniya, 1973, Volume 18, Issue 3, Pages 662–668 (Mi tvp2747)  

This article is cited in 50 scientific papers (total in 50 papers)

Short Communications

On estimation of functionals of the probability density function and its derivatives

Yu. G. Dmitriev, F. P. Tarasenko

Tomsk
Abstract: For functionals of the type $I=\int_{-\infty}^\infty H(f(y)),f'(y),\dots,f^{(r)}(y))\,dy$ the estimates $I_N=\int_{-k_N}^{k_N}H(f_N(y),\dots,f_N^{(r)}(y))\,dy$ are considered. Here $f_N(y),\dots,f_N^{(r)}(y)$ are nonparametric estimates of the density and of its derivatives introduced by Rosenblatt and studied by Parzen, Bhattacharya, Nadaraya and others. Theorems on convergence of the estimates with probability one are proved for Fisher's information, the entropy and the integral of the squared density. Convergence in probability are also investigated.
Received: 20.12.1971
English version:
Theory of Probability and its Applications, 1974, Volume 18, Issue 3, Pages 628–633
DOI: https://doi.org/10.1137/1118083
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yu. G. Dmitriev, F. P. Tarasenko, “On estimation of functionals of the probability density function and its derivatives”, Teor. Veroyatnost. i Primenen., 18:3 (1973), 662–668; Theory Probab. Appl., 18:3 (1974), 628–633
Citation in format AMSBIB
\Bibitem{DmiTar73}
\by Yu.~G.~Dmitriev, F.~P.~Tarasenko
\paper On estimation of functionals of the probability density function and its derivatives
\jour Teor. Veroyatnost. i Primenen.
\yr 1973
\vol 18
\issue 3
\pages 662--668
\mathnet{http://mi.mathnet.ru/tvp2747}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=359157}
\zmath{https://zbmath.org/?q=an:0301.62020}
\transl
\jour Theory Probab. Appl.
\yr 1974
\vol 18
\issue 3
\pages 628--633
\crossref{https://doi.org/10.1137/1118083}
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  • https://www.mathnet.ru/eng/tvp/v18/i3/p662
  • This publication is cited in the following 50 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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