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On the LIL for Self-Normalized Sums of IID Random Variables

Author

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  • Evarist Giné
  • David M. Mason

Abstract

Let $$X,X_i ,i \in \mathbb{N},$$ be i.i.d. random variables and let, for each $$n \in \mathbb{N},S_n = \sum\nolimits_{i = 1}^n {X_i }$$ and $$V_n^2 = \sum\nolimits_{i = 1}^n {X_i^2 }$$ . It is shown that $$\lim \sup _{n \to \infty } {{|S_n |} \mathord{\left/ {\vphantom {{|S_n |} {(V_n \sqrt {\log \log n} )

Suggested Citation

  • Evarist Giné & David M. Mason, 1998. "On the LIL for Self-Normalized Sums of IID Random Variables," Journal of Theoretical Probability, Springer, vol. 11(2), pages 351-370, April.
    • Handle: RePEc:spr:jotpro:v:11:y:1998:i:2:d:10.1023_a:1022675620729
    DOI: 10.1023/A:1022675620729
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    Cited by:

    1. Xia Chen, 1999. "The Law of the Iterated Logarithm for Functionals of Harris Recurrent Markov Chains: Self Normalization," Journal of Theoretical Probability, Springer, vol. 12(2), pages 421-445, April.
    2. David M. Mason, 2013. "Erratum to: The Asymptotic Distribution of Self-Normalized Triangular Arrays," Journal of Theoretical Probability, Springer, vol. 26(2), pages 589-593, June.

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