RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 2012, Volume 91, Issue 4, Pages 551–562 (Mi mz9325)  

This article is cited in 2 scientific papers (total in 2 papers)

Properties of the Székely–Móri Symmetry Criterion Statistics in the Case of Binary Vectors

A. M. Zubkova, D. O. Men'sheninb

a Steklov Mathematical Institute, Russian Academy of Sciences
b M. V. Lomonosov Moscow State University

Abstract: We study the properties of the statistics of the Székely–Móri criterion for the symmetry of a distribution in Euclidean space for the class of discrete distributions concentrated on the set of vertices of the $d$-dimensional cube. We obtain exact and asymptotic (as $d\to\infty$) formulas for the first moments of the statistic, prove limit theorems, and give examples showing how the efficiency of the criterion depends on the form of the distribution.

Keywords: Székely–Móri symmetry criterion, random vector, discrete distribution, normal distribution, limit distribution, $U$-statistics

DOI: https://doi.org/10.4213/mzm9325

Full text: PDF file (464 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2012, 91:4, 517–527

Bibliographic databases:

Document Type: Article
UDC: 519.22
Received: 17.11.2010

Citation: A. M. Zubkov, D. O. Men'shenin, “Properties of the Székely–Móri Symmetry Criterion Statistics in the Case of Binary Vectors”, Mat. Zametki, 91:4 (2012), 551–562; Math. Notes, 91:4 (2012), 517–527

Citation in format AMSBIB
\Bibitem{ZubMen12}
\by A.~M.~Zubkov, D.~O.~Men'shenin
\paper Properties of the Sz\'ekely--M\'ori Symmetry Criterion Statistics in the Case of Binary Vectors
\jour Mat. Zametki
\yr 2012
\vol 91
\issue 4
\pages 551--562
\mathnet{http://mi.mathnet.ru/mz9325}
\crossref{https://doi.org/10.4213/mzm9325}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3201455}
\elib{http://elibrary.ru/item.asp?id=20731515}
\transl
\jour Math. Notes
\yr 2012
\vol 91
\issue 4
\pages 517--527
\crossref{https://doi.org/10.1134/S0001434612030261}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000303478900026}
\elib{http://elibrary.ru/item.asp?id=17983961}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84860376365}


Linking options:
  • http://mi.mathnet.ru/eng/mz9325
  • https://doi.org/10.4213/mzm9325
  • http://mi.mathnet.ru/eng/mz/v91/i4/p551

    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. Szekely G.J., Rizzo M.L., “Energy Statistics: a Class of Statistics Based on Distances”, J. Stat. Plan. Infer., 143:8 (2013), 1249–1272  crossref  mathscinet  zmath  isi  elib  scopus
    2. Rizzo M.L., Szekely G.J., “Energy distance”, Wiley Interdiscip. Rev.-Comput. Stat., 8:1 (2016), 27–38  crossref  mathscinet  isi  elib  scopus
  • Математические заметки Mathematical Notes
    Number of views:
    This page:190
    Full text:15
    References:24
    First page:19

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018