Nonuniform Berry-Esseen bound for self-normalized martingales

Nonuniform Berry-Esseen bound for self-normalized martingales

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...

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Hauptverfasser: Wu, Songqi, Kong, Lingjie
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Probability
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Zusammenfassung: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.
DOI:10.48550/arxiv.2104.14063