arXiv:math/0503660 Abstract

arXiv:math/0503660 [math.PR]Abstract References Reviews Resources

Sectorial convergence of U-statistics

Published 2005-03-29Version 1

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.

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

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

DOI: 10.1214/009117904000001080

Categories: math.PR

Subjects: 60F15, 60E15

Keywords: sectorial convergence, sure convergence, linear sector, similar results, random variables

Tags: journal article

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