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., 2002, Volume 47, Issue 1, Pages 159–166 (Mi tvp3378)  

Short Communications

The unimprovability of moment estimates

A. V. Makrushin


Abstract: Let $\eta$ be a nonnegative random variable. A. M. Zubkov in [Obozrenie Prikl. Prom. Mat., 1 (1994), pp. 638–666 (in Russian)] obtained upper and low estimates for $P\{\eta>0\}$ in the form of a ratio of determinants formed by moments of $\eta$. The low estimates are always nonnegative and the upper estimates can take values from ${[1,\infty)}$. We show that the low and the upper estimates are unimprovable; i.e., for any random variable $\eta\ge 0$ there exist random variables $\zeta\geq 0$ and $\xi\geq 0$ with the same first moments as $\eta$ have, for which $P\{\zeta>0\}$ coincides with the low estimate and $P\{\xi>0\}$ coincides with the minimum of the upper estimate and 1.

Keywords: unimprovability of estimates, moments, moment problem, moment estimates.

DOI: https://doi.org/10.4213/tvp3378

Full text: PDF file (758 kB)

English version:
Theory of Probability and its Applications, 2003, 47:1, 164–171

Bibliographic databases:

Received: 10.04.2001

Citation: A. V. Makrushin, “The unimprovability of moment estimates”, Teor. Veroyatnost. i Primenen., 47:1 (2002), 159–166; Theory Probab. Appl., 47:1 (2003), 164–171

Citation in format AMSBIB
\Bibitem{Mak02}
\by A.~V.~Makrushin
\paper The unimprovability of moment estimates
\jour Teor. Veroyatnost. i Primenen.
\yr 2002
\vol 47
\issue 1
\pages 159--166
\mathnet{http://mi.mathnet.ru/tvp3378}
\crossref{https://doi.org/10.4213/tvp3378}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1978704}
\zmath{https://zbmath.org/?q=an:1033.60014}
\transl
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 1
\pages 164--171
\crossref{https://doi.org/10.1137/S0040585X97979536}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000183800400016}


Linking options:
  • http://mi.mathnet.ru/eng/tvp3378
  • https://doi.org/10.4213/tvp3378
  • http://mi.mathnet.ru/eng/tvp/v47/i1/p159

    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
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:131
    Full text:46

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