The Annals of Statistics

Asymptotic Distribution of Symmetric Statistics

H. Rubin and R. A. Vitale

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Abstract

Sequences of $m$th order symmetric statistics are examined for convergence in law. Under appropriate conditions, a limiting distribution exists and is equivalent to that of a linear combination of products of Hermite polynomials of independent $N(0, 1)$ random variables. Connections with the work of von Mises, Hoeffding, and Filippova are noted.

Article information

Source
Ann. Statist., Volume 8, Number 1 (1980), 165-170.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344898

Digital Object Identifier
doi:10.1214/aos/1176344898

Mathematical Reviews number (MathSciNet)
MR557561

Zentralblatt MATH identifier
0422.62016

JSTOR
links.jstor.org

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

Keywords
Symmetric statistics Hermite polynomials von Mises statistics $U$-statistics

Citation

Rubin, H.; Vitale, R. A. Asymptotic Distribution of Symmetric Statistics. Ann. Statist. 8 (1980), no. 1, 165--170. doi:10.1214/aos/1176344898. https://projecteuclid.org/euclid.aos/1176344898


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