Berry–Esseen Bounds for Self-Normalized Martingales

@article{Fan2017BerryEsseenBF,
  title={Berry–Esseen Bounds for Self-Normalized Martingales},
  author={Xiequan Fan and Q. Shao},
  journal={Communications in Mathematics and Statistics},
  year={2017},
  volume={6},
  pages={13-27}
}
  • Xiequan Fan, Q. Shao
  • Published 2017
  • Mathematics
  • Communications in Mathematics and Statistics
    • 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. 
    View on Springer
    arxiv.org
    1 Citations
    One Citation
    Citation Type

    Citation Type

    A Complete Bibliography of Publications in Communications in Mathematics and Statistics
    • 1
    • PDF

    References

    SHOWING 1-10 OF 16 REFERENCES
    The Berry-Esseen bound for student's statistic
    • 94
    • Highly Influential
    A Berry-Esséen bound for student's statistic in the non-I.I.D. case
    • 44
    • Highly Influential
    • PDF
    On the Rate of Convergence in the Central Limit Theorem for Martingales with Discrete and Continuous Time
    • 67
    • Highly Influential
    Self-Normalized Processes: Limit Theory and Statistical Applications
    • 182
    Donsker's theorem for self-normalized partial sums processes
    • 126
    A Cramér Type Large Deviation Result for Student's t-Statistic
    • 67
    Self-normalized Cramér-type large deviations for independent random variables
    • 146
    • PDF
    Self-normalization: Taming a wild population in a heavy-tailed world
    • 5
    When is the Student $t$-statistic asymptotically standard normal?
    • 212
    • PDF
    Self-normalized limit theorems: A survey
    • 30
    • Highly Influential