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More on complete convergence for arrays

Author

Listed:
  • Sung, Soo Hak
  • Volodin, Andrei I.
  • Hu, Tien-Chung

Abstract

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.

Suggested Citation

  • Sung, Soo Hak & Volodin, Andrei I. & Hu, Tien-Chung, 2005. "More on complete convergence for arrays," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 303-311, March.
    • Handle: RePEc:eee:stapro:v:71:y:2005:i:4:p:303-311
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    References listed on IDEAS

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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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    Citations

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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. 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.
    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. Sung, Soo Hak, 2007. "Complete convergence for weighted sums of random variables," Statistics & Probability Letters, Elsevier, vol. 77(3), pages 303-311, February.
    5. Xuejun Wang & Yi Wu & Shuhe Hu, 2016. "Exponential probability inequality for $$m$$ m -END random variables and its applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 127-147, February.
    6. 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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    1. 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.
    2. Kuczmaszewska, Anna, 2007. "On complete convergence for arrays of rowwise dependent random variables," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1050-1060, June.
    3. Xuejun Wang & Yi Wu & Shuhe Hu, 2016. "Exponential probability inequality for $$m$$ m -END random variables and its applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 127-147, February.
    4. Kuczmaszewska, Anna, 2004. "On some conditions for complete convergence for arrays," Statistics & Probability Letters, Elsevier, vol. 66(4), pages 399-405, March.
    5. Sung, Soo Hak, 2007. "Complete convergence for weighted sums of random variables," Statistics & Probability Letters, Elsevier, vol. 77(3), pages 303-311, February.

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