Open Access
February, 1977 On the Berry-Esseen Theorem for $U$-Statistics
Y.-K. Chan, John Wierman
Ann. Probab. 5(1): 136-139 (February, 1977). DOI: 10.1214/aop/1176995897


Assuming the existence of fourth moment only, we prove the Berry-Esseen theorem for $U$-statistics. Assuming the third absolute moment, we obtain the order bound $O(n^{-\frac{1}{2}} \log^{\frac{1}{3}}n)$. This improves earlier results of Bickel, and Grams and Serfling.


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Y.-K. Chan. John Wierman. "On the Berry-Esseen Theorem for $U$-Statistics." Ann. Probab. 5 (1) 136 - 139, February, 1977.


Published: February, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0381.60022
MathSciNet: MR433551
Digital Object Identifier: 10.1214/aop/1176995897

Primary: 60F07

Keywords: $U$-statistics , Berry-Esseen bounds

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 1 • February, 1977
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