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The Marcinkiewics–Zygmund strong law of large numbers for dependent random variables

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  • Boukhari, Fakhreddine

Abstract

In this paper, we provide a necessary and sufficient condition for the Marcinkiewics–Zygmund strong law of large numbers to hold, for an AANA sequence of non-identically distributed random variables. Our results complete and strengthen a similar result due to Chandra and Ghosal. We also show that the obtained method applies in the NSD setting.

Suggested Citation

  • Boukhari, Fakhreddine, 2020. "The Marcinkiewics–Zygmund strong law of large numbers for dependent random variables," Statistics & Probability Letters, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:stapro:v:161:y:2020:i:c:s0167715220300304
    DOI: 10.1016/j.spl.2020.108727
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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. Christofides, Tasos C. & Vaggelatou, Eutichia, 2004. "A connection between supermodular ordering and positive/negative association," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 138-151, January.
    3. Eghbal, N. & Amini, M. & Bozorgnia, A., 2011. "On the Kolmogorov inequalities for quadratic forms of dependent uniformly bounded random variables," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1112-1120, August.
    4. 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.
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    Cited by:

    1. Bernou, Ismahen & Boukhari, Fakhreddine, 2022. "Limit theorems for dependent random variables with infinite means," Statistics & Probability Letters, Elsevier, vol. 189(C).

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