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The Hájeck-Rényi inequality for the NA random variables and its application

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  • Liu, Jingjun
  • Gan, Shixin
  • Chen, Pingyan

Abstract

In this paper, we obtain the Hajeck-Rényi inequality and discuss the Marcinkiewicz strong law of large numbers for negatively associated random variables. In particular, the classical Marcinkiewicz strong law of large numbers for independent and identically distributed random variables is generalized to the case of negatively associated random variables.

Suggested Citation

  • Liu, Jingjun & Gan, Shixin & Chen, Pingyan, 1999. "The Hájeck-Rényi inequality for the NA random variables and its application," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 99-105, May.
    • Handle: RePEc:eee:stapro:v:43:y:1999:i:1:p:99-105
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    References listed on IDEAS

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    1. 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.
    2. Shixin, Gan, 1997. "The Hájek-Rényi inequality for Banach space valued martingales and the p smoothness of Banach spaces," Statistics & Probability Letters, Elsevier, vol. 32(3), pages 245-248, March.
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    Cited by:

    1. Yu Miao & Fangfang Zhao & Ke Wang & Yanping Chen, 2013. "Asymptotic normality and strong consistency of LS estimators in the EV regression model with NA errors," Statistical Papers, Springer, vol. 54(1), pages 193-206, February.
    2. Chen, Pingyan & Gan, Shixin, 2008. "On moments of the maximum of normed partial sums of [rho] -mixing random variables," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1215-1221, August.
    3. Shuhe, Hu & Ming, Hu, 2006. "A general approach rate to the strong law of large numbers," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 843-851, April.
    4. Boukhari, Fakhreddine, 2020. "The Marcinkiewics–Zygmund strong law of large numbers for dependent random variables," Statistics & Probability Letters, Elsevier, vol. 161(C).
    5. Sung, Soo Hak, 2008. "A note on the Hájek-Rényi inequality for associated random variables," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 885-889, May.
    6. Li, Yun-Xia & Wang, Jian-Feng, 2008. "An almost sure central limit theorem for products of sums under association," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 367-375, March.

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