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January, 1973 Convergence Rates for $U$-Statistics and Related Statistics
William F. Grams, R. J. Serfling
Ann. Statist. 1(1): 153-160 (January, 1973). DOI: 10.1214/aos/1193342392

Abstract

Bounds are provided for the rates of convergence in the central limit theorem and the strong law of large numbers for $U$-statistics. The results are obtained by establishing suitable bounds upon the moments of the difference between a $U$-statistic and its projection. Analogous conclusions for the associated von Mises statistical functions are indicated. Statistics considered for exemplification are the sample variance and the Wilcoxon two-sample statistic.

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William F. Grams. R. J. Serfling. "Convergence Rates for $U$-Statistics and Related Statistics." Ann. Statist. 1 (1) 153 - 160, January, 1973. https://doi.org/10.1214/aos/1193342392

Information

Published: January, 1973
First available in Project Euclid: 25 October 2007

zbMATH: 0322.62053
MathSciNet: MR336788
Digital Object Identifier: 10.1214/aos/1193342392

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 1 • January, 1973
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