Short Communications

Berry–Esseen inequalities for $U$-statistics

L. V. Gadasina

Petersburg State Transport University

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

DOI: 10.4213/tvp305

 English version: Theory of Probability and its Applications, 2004, 48:1, 147–152

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