The Annals of Probability

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

R. N. Bhattacharya and M. L. Puri

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62G05: Estimation 62G10: Hypothesis testing

Keywords
$V$-Statistics $U$-statistics Edgeworth expansion

Citation

Bhattacharya, R. N.; Puri, M. L. On the Order of Magnitude of Cumulants of Von Mises Functionals and Related Statistics. Ann. Probab. 11 (1983), no. 2, 346--354. doi:10.1214/aop/1176993600. https://projecteuclid.org/euclid.aop/1176993600


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