Sectorial convergence of U-statistics
Anda Gadidov
Source: Ann. Probab. Volume 33, Number 2
(2005), 816-822.
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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Permanent link to this document: http://projecteuclid.org/euclid.aop/1109868601
Digital Object Identifier: doi:10.1214/009117904000001080
Mathematical Reviews number (MathSciNet): MR2123211
Zentralblatt MATH identifier: 02164483
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Project Euclid: euclid.aop/1019160513
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