## The Annals of Probability

### On the Order of Magnitude of Cumulants of Von Mises Functionals and Related Statistics

#### Abstract

It is shown that under appropriate conditions the $s$th cumulant of a von Mises statistic or a $U$ (or $V$) statistic is $O(n^{-s + 1}), s \geq 2$, as the sample size $n$ goes to infinity. A possible route toward the derivation of an asymptotic expansion of the characteristic function is indicated.

#### Article information

Source
Ann. Probab., Volume 11, Number 2 (1983), 346-354.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176993600

Digital Object Identifier
doi:10.1214/aop/1176993600

Mathematical Reviews number (MathSciNet)
MR690132

Zentralblatt MATH identifier
0527.62025

JSTOR