Sectorial convergence of U-statistics
Probability
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0503660,
title = {Sectorial convergence of U-statistics},
author = {Anda Gadidov},
journal= {arXiv preprint arXiv:math/0503660},
year = {2007}
}
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)