On a multivariate version of Bernstein's inequality
Probability
2007-05-23 v1
Abstract
We prove a multivariate version of Bernstein's inequality about the probability that degenerate -statistics take a value larger than some number . This is an improvement of former estimates for the same problem which yields an asymptotically sharp estimate for not too large numbers . This paper also contains an analogous bound about the distribution of multiple Wiener-Ito integrals. Their comparison shows that our results are sharp. The proofs are based on good estimates about high moments of multiple random integrals. They are obtained by means of a diagram formula which enables us to express the product of multiple random integrals as the sum of such expressions.
Cite
@article{arxiv.math/0411287,
title = {On a multivariate version of Bernstein's inequality},
author = {P. Major},
journal= {arXiv preprint arXiv:math/0411287},
year = {2007}
}