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More on complete convergence for arrays


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  • Sung, Soo Hak
  • Volodin, Andrei I.
  • Hu, Tien-Chung
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    A complete convergence theorem for arrays of rowwise independent random variables was proposed by Hu et al. (Statist. Probab. Lett. 38 (1998) 27). Two years later, Hu and Volodin (Statist. Probab. Lett. 47 (2000) 209) imposed one additional condition in addendum to the paper. In this paper, we prove the complete convergence theorem without the additional condition.

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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 71 (2005)
    Issue (Month): 4 (March)
    Pages: 303-311

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    Handle: RePEc:eee:stapro:v:71:y:2005:i:4:p:303-311

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    Keywords: Arrays Rowwise independence Sums of independent random variables Complete convergence;


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    1. Hu, T. -C. & Szynal, D. & Volodin, A. I., 1998. "A note on complete convergence for arrays," Statistics & Probability Letters, Elsevier, vol. 38(1), pages 27-31, May.
    2. Kuczmaszewska, Anna, 2004. "On some conditions for complete convergence for arrays," Statistics & Probability Letters, Elsevier, vol. 66(4), pages 399-405, March.
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    Cited by:
    1. Stoica, George, 2008. "The Baum-Katz theorem for bounded subsequences," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 924-926, May.
    2. Sung, Soo Hak, 2007. "Complete convergence for weighted sums of random variables," Statistics & Probability Letters, Elsevier, vol. 77(3), pages 303-311, February.
    3. Kuczmaszewska, Anna, 2007. "On complete convergence for arrays of rowwise dependent random variables," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1050-1060, June.
    4. Kruglov, Victor M. & Volodin, Andrei I. & Hu, Tien-Chung, 2006. "On complete convergence for arrays," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1631-1640, September.
    5. Hernández, Víctor & Urmeneta, Henar, 2006. "Convergence rates for the law of large numbers for arrays," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1714-1722, October.


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