The Annals of Statistics

An Edgeworth Expansion for $U$-Statistics

H. Callaert, P. Janssen, and N. Veraverbeke

Full-text: Open access

Abstract

It is shown that, under some regularity conditions on the kernel, a one-sample $U$-statistic with kernel of degree two admits an asymptotic expansion with remainder term $o(N^{-1})$.

Article information

Source
Ann. Statist., Volume 8, Number 2 (1980), 299-312.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344955

Digital Object Identifier
doi:10.1214/aos/1176344955

Mathematical Reviews number (MathSciNet)
MR560731

Zentralblatt MATH identifier
0428.62016

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62E20: Asymptotic distribution theory

Keywords
Asymptotic expansion Gini's mean difference sample variance $U$-statistic

Citation

Callaert, H.; Janssen, P.; Veraverbeke, N. An Edgeworth Expansion for $U$-Statistics. Ann. Statist. 8 (1980), no. 2, 299--312. doi:10.1214/aos/1176344955. https://projecteuclid.org/euclid.aos/1176344955


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