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arXiv · 1712.03667

Berry-Esseen bounds for self-normalized martingales

Xiequan Fan·Qi-Man Shao
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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.

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Xiequan Fan, Qi-Man Shao. 2017-12-11. Berry-Esseen bounds for self-normalized martingales. https://arxiv.org/abs/1712.03667

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