This article is cited in 2 papers

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

A. M. Zubkov^a, D. O. Men'shenin<sup>b

a</sup> 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.

UDC: 519.22

Received: 17.11.2010

DOI: 10.4213/mzm9325

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

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