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March 2005 Sectorial convergence of U-statistics
Anda Gadidov
Ann. Probab. 33(2): 816-822 (March 2005). DOI: 10.1214/009117904000001080

Abstract

In this note we show that almost sure convergence to zero of symmetrized U-statistics indexed by a linear sector in ℤd+ is equivalent to convergence along the diagonal of ℤd+, as it is considered in Latała and Zinn [Ann. Probab. 28 (2000) 1908–1924]. Comparisons with similar results for sums of multi-indexed i.i.d. random variables are also made.

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Anda Gadidov. "Sectorial convergence of U-statistics." Ann. Probab. 33 (2) 816 - 822, March 2005. https://doi.org/10.1214/009117904000001080

Information

Published: March 2005
First available in Project Euclid: 3 March 2005

zbMATH: 1066.60032
MathSciNet: MR2123211
Digital Object Identifier: 10.1214/009117904000001080

Subjects:
Primary: 60F15
Secondary: 60E15

Keywords: Decoupling , Rademacher sequence , Strong law of large numbers , U-statistics

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 2 • March 2005
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