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June, 1984 Invariance Principle for Symmetric Statistics
Avi Mandelbaum, Murad S. Taqqu
Ann. Statist. 12(2): 483-496 (June, 1984). DOI: 10.1214/aos/1176346501

Abstract

We derive invariance principles for processes associated with symmetric statistics of arbitrary order. Using a Poisson sample size, such processes can be viewed as functionals of a Poisson Point Process. Properly normalized, these functionals converge in distribution to functionals of a Gaussian random measure associated with the distribution of the observations. We thus obtain a natural description of the limiting process in terms of multiple Wiener integrals. The results are used to derive asymptotic expansions of processes arising from arbitrary square integrable $U$-statistics.

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Avi Mandelbaum. Murad S. Taqqu. "Invariance Principle for Symmetric Statistics." Ann. Statist. 12 (2) 483 - 496, June, 1984. https://doi.org/10.1214/aos/1176346501

Information

Published: June, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0547.60039
MathSciNet: MR740907
Digital Object Identifier: 10.1214/aos/1176346501

Subjects:
Primary: 60F17
Secondary: 60G99, 60K99, 62E20, 62G05

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 2 • June, 1984
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