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Precise asymptotics in some strong limit theorems for multidimensionally indexed random variables

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  • Gut, Allan
  • Spataru, Aurel

Abstract

Consider Z+d (d[greater-or-equal, slanted]2)--the positive d-dimensional lattice points with partial ordering [less-than-or-equals, slant], let {Xk,k[set membership, variant]Z+d} be i.i.d. random variables with mean 0, and set Sn=[summation operator]k[less-than-or-equals, slant]nXk, n[set membership, variant]Z+d. We establish precise asymptotics for [summation operator]nnr/p-2P(Sn[greater-or-equal, slanted][var epsilon]n1/p), and for , (0[less-than-or-equals, slant][delta][less-than-or-equals, slant]1) as [var epsilon][downward right arrow]0, and for as .

Suggested Citation

  • Gut, Allan & Spataru, Aurel, 2003. "Precise asymptotics in some strong limit theorems for multidimensionally indexed random variables," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 398-422, August.
    • Handle: RePEc:eee:jmvana:v:86:y:2003:i:2:p:398-422
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    References listed on IDEAS

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    1. Chen, Robert, 1978. "A remark on the tail probability of a distribution," Journal of Multivariate Analysis, Elsevier, vol. 8(2), pages 328-333, June.
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    Cited by:

    1. Fa-mei Zheng & Qing-pei Zang, 2015. "A general pattern of asymptotic behavior of the R/S statistics for linear processes," Statistical Papers, Springer, vol. 56(1), pages 191-204, February.
    2. He, Jianjun, 2012. "An estimate of the remainder of a limit theorem," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 478-487.
    3. Sergio Alvarez-Andrade & Salim Bouzebda, 2014. "Asymptotic results for hybrids of empirical and partial sums processes," Statistical Papers, Springer, vol. 55(4), pages 1121-1143, November.
    4. A. Spătaru, 2004. "Exact Asymptotics in log log Laws for Random Fields," Journal of Theoretical Probability, Springer, vol. 17(4), pages 943-965, October.
    5. Cai, Guang-hui & Wang, Jian-Feng, 2009. "Uniform bounds in normal approximation under negatively associated random fields," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 215-222, January.

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