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Teoriya Veroyatnostei i ee Primeneniya, 2003, Volume 48, Issue 1, Pages 151–155
DOI: https://doi.org/10.4213/tvp305 (Mi tvp305) 		 
Short Communications

Berry–Esseen inequalities for $U$-statistics

L. V. Gadasina

Petersburg State Transport University
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DOI: https://doi.org/10.4213/tvp305
Abstract: We obtain a Berry–Esseen boundary for nondegenerate $U$-statistics of power 2 constructed by independent and not necessarily identically distributed random variables assuming finiteness of the absolute third moments for the first family of the canonical functions and the absolute moments of order $\frac 53$ for the second family of the canonical functions in the Höeffding expansion.
Keywords: $U$-statistic, Berry–Esseen inequality, rate of convergence.
Received: 16.07.2001
Revised: 28.09.2001
English version:
Theory of Probability and its Applications, 2004, Volume 48, Issue 1, Pages 147–152
DOI: https://doi.org/10.1137/S0040585X980208
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: L. V. Gadasina, “Berry–Esseen inequalities for $U$-statistics”, Teor. Veroyatnost. i Primenen., 48:1 (2003), 151–155; Theory Probab. Appl., 48:1 (2004), 147–152
Citation in format AMSBIB
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\jour Theory Probab. Appl.
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