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On the weak laws of large numbers for sums of negatively associated random vectors in Hilbert spaces

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  • Hien, N.T.T.
  • Thanh, L.V.

Abstract

This note establishes the weak law of large numbers for sums of negatively associated random vectors in Hilbert spaces. Illustrative examples are provided, one of which shows that the conditions for the weak law of large numbers cannot be dispensed with.

Suggested Citation

  • Hien, N.T.T. & Thanh, L.V., 2015. "On the weak laws of large numbers for sums of negatively associated random vectors in Hilbert spaces," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 236-245.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:236-245
    DOI: 10.1016/j.spl.2015.08.030
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    References listed on IDEAS

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    1. Chen, Xiaohong & White, Halbert, 1998. "Central Limit And Functional Central Limit Theorems For Hilbert-Valued Dependent Heterogeneous Arrays With Applications," Econometric Theory, Cambridge University Press, vol. 14(2), pages 260-284, April.
    2. Zhang, Li-Xin, 2001. "Strassen's law of the iterated logarithm for negatively associated random vectors," Stochastic Processes and their Applications, Elsevier, vol. 95(2), pages 311-328, October.
    3. Dehling, Herold & Sharipov, Olimjon Sh. & Wendler, Martin, 2015. "Bootstrap for dependent Hilbert space-valued random variables with application to von Mises statistics," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 200-215.
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    Cited by:

    1. Chang, Mengmeng & Miao, Yu, 2023. "Generalized weak laws of large numbers in Hilbert spaces," Statistics & Probability Letters, Elsevier, vol. 197(C).
    2. Miaomiao Wang & Shunping Zheng & Xuejun Wang, 2025. "Equivalent conditions of complete moment convergence for randomly weighted sums of random variables and some applications with random design," Statistical Papers, Springer, vol. 66(2), pages 1-33, February.

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