Berry-Esseen bounds for self-normalized martingales

Published 11 Dec 2017 in math.PR | (1712.03667v1)

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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