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Matematicheskie Zametki, 2012, Volume 91, Issue 4, Pages 551–562
DOI: https://doi.org/10.4213/mzm9325 (Mi mzm9325) 		 
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
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DOI: https://doi.org/10.4213/mzm9325
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→∞) 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.
Received: 17.11.2010
English version:
Mathematical Notes, 2012, Volume 91, Issue 4, Pages 517–527
DOI: https://doi.org/10.1134/S0001434612030261
Bibliographic databases:
Document Type: Article
UDC: 519.22
Language: Russian
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
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    • This publication is cited in the following 2 articles:
    1. Rizzo M.L., Szekely G.J., “Energy distance”, Wiley Interdiscip. Rev.-Comput. Stat., 8:1 (2016), 27–38  crossref  mathscinet  isi  elib  scopus
    2. 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
    Citing articles in Google Scholar: Russian citations, English citations
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