Properties of the Székely-Móri symmetry criterion statistics in the case of binary vectors

Mathematical Notes

Volumn 91, Issue 3-4, 2012, Pages 517-527

  Zubkov, A M ^a   Men'shenin, D O ^b  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

discrete distribution; limit distribution; normal distribution; random vector; Sz kely M ri symmetry criterion; U statistics

Indexed keywords

EID: 84860376365     PISSN: 00014346     EISSN: None     Source Type: Journal    
DOI: 10.1134/S0001434612030261     Document Type: Article

References (6)

1. G. J. Székely and T. F. Móri, "A characteristic measure of asymmetry and its application for testing diagonal symmetry," Comm. Statist. Theory Methods 30(8-9), 1633-1639 (2001).
2. G. G. Gregory, "Large sample theory for U-statistics and tests of fit," Ann. Statist. 5(1), 110-123 (1977).
3. V. S. Korolyuk and Yu. V. Borovskikh, The Theory of U-Statistics (Naukova Dumka, Kiev, 1989) [inRussian].
4. G. J. Székely and N. K. Bakirov, "Extremal probabilities for Gaussian quadratic forms," Probab. Theory Related Fields 126(2), 184-202 (2003).
5. W. Hoeffding, "A class of statistics with asymptotically normal distribution," Ann. Math. Statist. 19(3), 293-325 (1948).
6. D. O. Menshenin and A. M. Zubkov, "On the Székely-Móri asymmetry criterion statistics for binary vectors with independent components," Austrian J. Statist. 37(1), 137-144 (2008).