Open Access
Translator Disclaimer
January, 1980 Asymptotic Distribution of Symmetric Statistics
H. Rubin, R. A. Vitale
Ann. Statist. 8(1): 165-170 (January, 1980). DOI: 10.1214/aos/1176344898

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.

Citation

Download Citation

H. Rubin. R. A. Vitale. "Asymptotic Distribution of Symmetric Statistics." Ann. Statist. 8 (1) 165 - 170, January, 1980. https://doi.org/10.1214/aos/1176344898

Information

Published: January, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0422.62016
MathSciNet: MR557561
Digital Object Identifier: 10.1214/aos/1176344898

Subjects:
Primary: 60F05
Secondary: 62E20

Keywords: $U$-statistics , Hermite polynomials , symmetric statistics , von Mises statistics

Rights: Copyright © 1980 Institute of Mathematical Statistics

JOURNAL ARTICLE
6 PAGES


SHARE
Vol.8 • No. 1 • January, 1980
Back to Top