Berry–Esseen Bounds for Self-Normalized Martingales

@article{Fan2017BerryEsseenBF,
title={Berry–Esseen Bounds for Self-Normalized Martingales},
author={Xiequan Fan and Q. Shao},
journal={Communications in Mathematics and Statistics},
year={2017},
volume={6},
pages={13-27}
}

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.