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The Weak Convergence for Functions of Negatively Associated Random Variables

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  • Zhang, Li-Xin

Abstract

Let {Xn, n[greater-or-equal, slanted]1} be a sequence of stationary negatively associated random variables, Sj(l)=[summation operator]li=1 Xj+i, Sn=[summation operator]ni=1 Xi. Suppose that f(x) is a real function. Under some suitable conditions, the central limit theorem and the weak convergence for sumsare investigated. Applications to limiting distributions of estimators of Var Sn are also discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:78:y:2001:i:2:p:272-298
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    References listed on IDEAS

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    1. Peligrad, M. & Shao, Q. M., 1995. "Estimation of the Variance of Partial Sums for [rho]-Mixing Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 140-157, January.
    2. Peligard, Magda & Suresh, Ram, 1995. "Estimation of variance of partial sums of an associated sequence of random variables," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 307-319, April.
    3. 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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    Cited by:

    1. Zhang, Junjian, 2006. "Empirical likelihood for NA series," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 153-160, January.
    2. Wang, Jiang-Feng & Liang, Han-Ying, 2008. "A note on the almost sure central limit theorem for negatively associated fields," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1964-1970, September.
    3. Huang, Wei & Zhang, Lin-Xi, 2006. "Asymptotic normality for U-statistics of negatively associated random variables," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1125-1131, June.
    4. 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.
    5. Yongsong Qin & Yinghua Li & Weizhen Yang & Qingzhu Lei, 2011. "Confidence intervals for nonparametric regression functions under negatively associated errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 645-659.
    6. 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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