The optimal fourth moment theorem
Probability
2013-05-08 v1
Abstract
We compute the exact rates of convergence in total variation associated with the 'fourth moment theorem' by Nualart and Peccati (2005), stating that a sequence of random variables living in a fixed Wiener chaos verifies a central limit theorem (CLT) if and only if the sequence of the corresponding fourth cumulants converges to zero. We also provide an explicit illustration based on the Breuer-Major CLT for Gaussian-subordinated random sequences.
Cite
@article{arxiv.1305.1527,
title = {The optimal fourth moment theorem},
author = {Ivan Nourdin and Giovanni Peccati},
journal= {arXiv preprint arXiv:1305.1527},
year = {2013}
}
Comments
10 pages