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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}
}
R2 v1 2026-06-22T23:13:54.076Z