Sectorial convergence of U-statistics

Details Sectorial convergence of U-statistics Sectorial convergence of U-statistics

2005-03-29

arxiv.org/abs/math/0503660v1

Annals of Probability 2005, Vol. 33, No. 2, 816-822

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000001080 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117904000001080

In this note we show that almost sure convergence to zero of symmetrized
U-statistics indexed by a linear sector in Z^d_+ is equivalent to convergence
along the diagonal of Z^d_+, as it is considered in Lata\la 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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