Open Access
Translator Disclaimer
March, 1978 The Berry-Esseen Theorem for $U$-Statistics
Herman Callaert, Paul Janssen
Ann. Statist. 6(2): 417-421 (March, 1978). DOI: 10.1214/aos/1176344132

Abstract

Assuming only the existence of the third absolute moment we prove that $\sup_x |P(\sigma_n^{-1} U_n \leqq x) - \Phi (x)| \leqq C_{\nu_3\sigma_g}^{-3}n^{-\frac{1}{2}}$ where $U_n$ is a $U$-statistic. This concludes a series of investigations on the Berry-Esseen theorem for $U$-statistics by Grams and Serfling, Bickel, and Chan and Wierman.

Citation

Download Citation

Herman Callaert. Paul Janssen. "The Berry-Esseen Theorem for $U$-Statistics." Ann. Statist. 6 (2) 417 - 421, March, 1978. https://doi.org/10.1214/aos/1176344132

Information

Published: March, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0393.60022
MathSciNet: MR464359
Digital Object Identifier: 10.1214/aos/1176344132

Subjects:
Primary: 60F05

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

Rights: Copyright © 1978 Institute of Mathematical Statistics

JOURNAL ARTICLE
5 PAGES


SHARE
Vol.6 • No. 2 • March, 1978
Back to Top