The Annals of Statistics

On the Berry-Esseen Theorem for Random $U$-Statistics

Ibrahim A. Ahmad

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Abstract

A Berry-Esseen theorem for $U$-statistics when the sample size is random is presented for the case when the random size is independent of the observations. This result extends the work of Callaert and Janssen. As an application of the special case of sample means, a rate of convergence to normality is obtained for the supercritical Galton-Watson process. Other possible applications are in sequential analysis.

Article information

Source
Ann. Statist., Volume 8, Number 6 (1980), 1395-1398.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345212

Digital Object Identifier
doi:10.1214/aos/1176345212

Mathematical Reviews number (MathSciNet)
MR594656

Zentralblatt MATH identifier
0463.60028

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 62L10: Sequential analysis

Keywords
Berry-Esseen theorem $U$-statistics random indicies Galton-Watson process supercritical sequential analysis

Citation

Ahmad, Ibrahim A. On the Berry-Esseen Theorem for Random $U$-Statistics. Ann. Statist. 8 (1980), no. 6, 1395--1398. doi:10.1214/aos/1176345212. https://projecteuclid.org/euclid.aos/1176345212


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