Geodesic
Properties of the Sz\'ekely--M\'ori Symmetry Criterion Statistics in the Case of Binary Vectors
Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 551-562

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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, $U$-statistics.
Mots-clés : normal distribution, limit distribution 
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     author = {A. M. Zubkov and D. O. Men'shenin},
     title = {Properties of the {Sz\'ekely--M\'ori} {Symmetry} {Criterion} {Statistics} in the {Case} of {Binary} {Vectors}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {551--562},
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A. M. Zubkov; D. O. Men'shenin. Properties of the Sz\'ekely--M\'ori Symmetry Criterion Statistics in the Case of Binary Vectors. Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 551-562. http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a7/