Nonuniform Berry-Esseen bound for self-normalized martingales

Songqi Wu; Lingjie Kong

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arXiv · 2104.14063

Nonuniform Berry-Esseen bound for self-normalized martingales

Songqi Wu·Lingjie Kong

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Abstract

We give a nonuniform Berry-Esseen bound for self-normalized martingales, which bridges the gap between the result of Haeusler (1988) and Fan and Shao (2018). The bound coincides with the nonuniform Berry-Esseen bound of Haeusler and Joos (1988) for standardized martingales. As a consequence, a Berry-Esseen bound is obtained.

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Songqi Wu, Lingjie Kong. 2021-04-29. Nonuniform Berry-Esseen bound for self-normalized martingales. https://arxiv.org/abs/2104.14063

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