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.
Bernstein type inequalities for self-normalized martingales with applications
New insights on concentration inequalities for self-normalized martingales
Nonuniform Berry-Esseen bound for self-normalized martingales
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