Nonuniform Berry-Esseen bound for self-normalized martingales

Published 29 Apr 2021 in math.PR | (2104.14063v1)

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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