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., 1982, Volume 27, Issue 3, Pages 514–524 (Mi tvp2383)  

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

On a density estimation within a class of entire functions

I. A. Ibragimova, R. Z. Has'minskiĭb

a Leningrad
b Moscow

Abstract: Let $X_1,…,X_n$ be i. i. d. random variables with values in $R^k$ and $p(x)$ be their density. Denote by $\Sigma(\mathbf K)$ the class of density functions such that their characteristic functions have symmetric compact support $\mathbf K$. For an arbitrary estimator $T_n(x)$ consider a function
$$ \Delta_n^2(T_n,p)=\mathbf E_p\|T_n-p\|_2^2, $$
where $\|\cdot\|_2$ is the $\mathscr L_2$-norm, $\mathbf E_p(\cdot)$ is the expectation with respect to the measure generated by $X_1,…,X_n$. We prove the equality
$$ \lim_{n\to\infty}[n\inf_{T_n}\sup_{p\in\Sigma(\mathbf K)}\Delta_n^2(T_n,p)]=\frac{\operatorname{mes}\mathbf K}{(2\pi)^k} $$
and some related results.

Full text: PDF file (581 kB)

English version:
Theory of Probability and its Applications, 1983, 27:3, 551–562

Bibliographic databases:

Received: 19.12.1980

Citation: I. A. Ibragimov, R. Z. Has'minskiǐ, “On a density estimation within a class of entire functions”, Teor. Veroyatnost. i Primenen., 27:3 (1982), 514–524; Theory Probab. Appl., 27:3 (1983), 551–562

Citation in format AMSBIB
\Bibitem{IbrKha82}
\by I.~A.~Ibragimov, R.~Z.~Has'minski{\v\i}
\paper On a~density estimation within a~class of entire functions
\jour Teor. Veroyatnost. i Primenen.
\yr 1982
\vol 27
\issue 3
\pages 514--524
\mathnet{http://mi.mathnet.ru/tvp2383}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=673923}
\zmath{https://zbmath.org/?q=an:0516.62043|0495.62047}
\transl
\jour Theory Probab. Appl.
\yr 1983
\vol 27
\issue 3
\pages 551--562
\crossref{https://doi.org/10.1137/1127062}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1983RJ51700009}


Linking options:
  • http://mi.mathnet.ru/eng/tvp2383
  • http://mi.mathnet.ru/eng/tvp/v27/i3/p514

    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. L. L. Boiko, “Wavelets and Estimation of Discontinuous Functions”, Problems Inform. Transmission, 40:3 (2004), 226–236  mathnet  crossref  mathscinet  zmath
    2. I. A. Ibragimov, “Analytical density estimation on the base of censured data”, J. Math. Sci. (N. Y.), 133:3 (2006), 1290–1297  mathnet  crossref  mathscinet  zmath  elib
    3. I. A. Ibragimov, “On estimation of multidimensional analytic distribution density by censored sample”, Theory Probab. Appl., 51:1 (2007), 142–154  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Holzmann H., Bissantz N., Munk A., “Density testing in a contaminated sample”, Journal of Multivariate Analysis, 98:1 (2007), 57–75  crossref  mathscinet  zmath  isi
    5. Efromovich S., “Adaptive estimation of and oracle inequalities for probability densities and characteristic functions”, Annals of Statistics, 36:3 (2008), 1127–1155  crossref  mathscinet  zmath  isi
    6. J. Math. Sci. (N. Y.), 163:3 (2010), 238–261  mathnet  crossref
    7. Cavalier L., Hengartner N., “Estimating linear functionals in Poisson mixture models”, Journal of Nonparametric Statistics, 21:6 (2009), 713–728  crossref  mathscinet  zmath  isi
    8. I. A. Ibragimov, “A generalization of Chentsov's projection estimates”, J. Math. Sci. (N. Y.), 204:1 (2015), 116–133  mathnet  crossref  mathscinet
    9. I. A. Ibragimov, “On the estimation of the intensity density function of Poisson random field outside of the observation region”, J. Math. Sci. (N. Y.), 214:4 (2016), 484–492  mathnet  crossref  mathscinet
    10. I. A. Ibragimov, “On the estimation of functions in Gaussian noise”, J. Math. Sci. (N. Y.), 238:4 (2019), 463–470  mathnet  crossref
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:203
    Full text:83

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020