Berry-Esseen bounds for self-normalized martingales

11 Dec 2017  ·  Fan Xiequan, Shao Qi-Man ·

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. read more

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Probability