Berry-Esseen bounds for self-normalized martingales
Probability
2019-07-04 v1
Abstract
A Berry-Esseen bound is obtained for self-normalized martingales under the assumption of finite moments. The bound coincides with the classical Berry-Esseen bound for standardized martingales. An example is given to show the optimality of the bound. Applications to Student's statistic and autoregressive process are also discussed.
Keywords
Cite
@article{arxiv.1712.03667,
title = {Berry-Esseen bounds for self-normalized martingales},
author = {Xiequan Fan and Qi-Man Shao},
journal= {arXiv preprint arXiv:1712.03667},
year = {2019}
}