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On the Self-Normalized Cramér-type Large Deviation

Author

Listed:
  • John Robinson

    (The University of Sydney)

  • Qiying Wang

    (The University of Sydney)

Abstract

For the self-normalized sum, $$S_n/V_n$$ , it is shown that $$P(S_n/V_n\ge x)/(1-\Phi(x))$$ converges to 1, uniformly in a region, under the optimal assumption that the sampled distribution is in the domain of attraction of the normal law. Bounds for this convergence are given and their applications to exponential non-uniform Berry–Esseen bound are also discussed.

Suggested Citation

  • John Robinson & Qiying Wang, 2005. "On the Self-Normalized Cramér-type Large Deviation," Journal of Theoretical Probability, Springer, vol. 18(4), pages 891-909, October.
    • Handle: RePEc:spr:jotpro:v:18:y:2005:i:4:d:10.1007_s10959-005-7531-5
    DOI: 10.1007/s10959-005-7531-5
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    Cited by:

    1. Qiying Wang, 2011. "Refined Self-normalized Large Deviations for Independent Random Variables," Journal of Theoretical Probability, Springer, vol. 24(2), pages 307-329, June.
    2. Pascal Beckedorf & Angelika Rohde, 2025. "Non-uniform Bounds and Edgeworth Expansions in Self-normalized Limit Theorems," Journal of Theoretical Probability, Springer, vol. 38(1), pages 1-94, March.

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