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Uniform bounds in normal approximation under negatively associated random fields

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  • Cai, Guang-hui
  • Wang, Jian-Feng

Abstract

We give uniform rates of convergence in the central limit theorem for negatively associated random fields with finite (2+[delta])th moment. These results are of an order close to the best possible if not the best possible. As application, we obtain precise asymptotics in the law of the logarithm.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:2:p:215-222
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    References listed on IDEAS

    as
    1. Zhang, Li-Xin & Wen, Jiwei, 2001. "A weak convergence for negatively associated fields," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 259-267, June.
    2. 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.
    3. Zhang, Li-Xin, 2001. "The Weak Convergence for Functions of Negatively Associated Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 78(2), pages 272-298, August.
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