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Berry-Esseen bounds for self-normalized martingales. (English) Zbl 1391.60089
Summary: 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.
60G42 Martingales with discrete parameter
60F05 Central limit and other weak theorems
60E15 Inequalities; stochastic orderings
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