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A Central Limit Theorem for Random Fields of Negatively Associated Processes

Author

Listed:
  • Ming Yuan

    (University of Wisconsin)

  • Chun Su

    (University of Science and Technology of China)

  • Taizhong Hu

    (University of Science and Technology of China)

Abstract

A central limit theorem for negatively associated random fields is established under the fairly general conditions. We use the finite second moment condition instead of the finite (2+δ)th moment condition used by Roussas.(15) A similar result is also given for positively associated sequences.

Suggested Citation

  • Ming Yuan & Chun Su & Taizhong Hu, 2003. "A Central Limit Theorem for Random Fields of Negatively Associated Processes," Journal of Theoretical Probability, Springer, vol. 16(2), pages 309-323, April.
    • Handle: RePEc:spr:jotpro:v:16:y:2003:i:2:d:10.1023_a:1023538824937
    DOI: 10.1023/A:1023538824937
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    References listed on IDEAS

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    1. Cai, Zongwu & Roussas, George G., 1998. "Kaplan-Meier Estimator under Association," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 318-348, November.
    2. Zhang, Li-Xin & Wen, Jiwei, 2001. "A weak convergence for negatively associated fields," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 259-267, June.
    3. Roussas, G. G., 1994. "Asymptotic Normality of Random Fields of Positively or Negatively Associated Processes," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 152-173, July.
    4. 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.
    5. Pruss, Alexander R. & Szynal, Dominik, 2000. "On the central limit theorem for negatively correlated random variables with negatively correlated squares," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 299-309, June.
    6. Shao, Qi-Man & Su, Chun, 1999. "The law of the iterated logarithm for negatively associated random variables," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 139-148, September.
    7. Matula, Przemyslaw, 1992. "A note on the almost sure convergence of sums of negatively dependent random variables," Statistics & Probability Letters, Elsevier, vol. 15(3), pages 209-213, October.
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