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Refined Self-normalized Large Deviations for Independent Random Variables

Author

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  • Qiying Wang

    (The University of Sydney)

Abstract

Let X 1,X 2,… , be independent random variables with EX i =0 and write $S_{n}=\sum_{i=1}^{n}X_{i}$ and $V_{n}^{2}=\sum_{i=1}^{n}X_{i}^{2}$ . This paper provides new refined results on the Cramér-type large deviation for the so-called self-normalized sum S n /V n . The major techniques used to derive these new findings are different from those used previously.

Suggested Citation

  • Qiying Wang, 2011. "Refined Self-normalized Large Deviations for Independent Random Variables," Journal of Theoretical Probability, Springer, vol. 24(2), pages 307-329, June.
    • Handle: RePEc:spr:jotpro:v:24:y:2011:i:2:d:10.1007_s10959-011-0347-6
    DOI: 10.1007/s10959-011-0347-6
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    References listed on IDEAS

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    1. 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.
    2. Qi-Man Shao, 1999. "A Cramér Type Large Deviation Result for Student's t-Statistic," Journal of Theoretical Probability, Springer, vol. 12(2), pages 385-398, April.
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    Cited by:

    1. Bing-Yi Jing & Qiying Wang & Wang Zhou, 2015. "Cramér-Type Moderate Deviation for Studentized Compound Poisson Sum," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1556-1570, December.

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