Properties of the Székely-Móri symmetry criterion statistics in the case of binary vectors
Андрей Михайлович Зубков, Dmitrii O. Menshenin · Mathematical Notes · 2012
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.