Uniform Limit Theorem and tail estimates for parametric u-statistics
Statistics Theory
2016-08-12 v1 Statistics Theory
Abstract
We deduce in this paper the sufficient conditions for weak convergence of centered and normed deviation of the u-statistics with values in the space of the real valued continuous function defined on some compact metric space. We obtain also a non-asymptotic and non-improvable up to multiplicative constant moment and exponential tail estimates for distribution for the uniform norm of centered and naturally normed deviation of u-statistics by means of its martingale representation. Our results are formulated in a very popular and natural terms of metric entropy in the distance (distances) generated by the introduced random processes (fields).
Cite
@article{arxiv.1608.03310,
title = {Uniform Limit Theorem and tail estimates for parametric u-statistics},
author = {E. Ostrovsky and L. Sirota},
journal= {arXiv preprint arXiv:1608.03310},
year = {2016}
}
Comments
arXiv admin note: text overlap with arXiv:1602.00175