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On the almost sure growth rate of sums of lower negatively dependent nonnegative random variables

Author

Listed:
  • Klesov, Oleg
  • Rosalsky, Andrew
  • Volodin, Andrei I.

Abstract

For a sequence of lower negatively dependent nonnegative random variables Xn,n[greater-or-equal, slanted]1 , conditions are provided under which almost surely where bn,n[greater-or-equal, slanted]1 is a nondecreasing sequence of positive constants. The results are new even when they are specialized to the case of nonnegative independent and identically distributed summands and bn=nr, n[greater-or-equal, slanted]1 where r>0.

Suggested Citation

  • Klesov, Oleg & Rosalsky, Andrew & Volodin, Andrei I., 2005. "On the almost sure growth rate of sums of lower negatively dependent nonnegative random variables," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 193-202, February.
    • Handle: RePEc:eee:stapro:v:71:y:2005:i:2:p:193-202
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    References listed on IDEAS

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    1. Rosalsky, Andrew, 1993. "On the almost certain limiting behavior of normed sums of identically distributed positive random variables," Statistics & Probability Letters, Elsevier, vol. 16(1), pages 65-70, January.
    2. Gut, Allan & Klesov, Oleg & Steinebach, Josef, 1997. "Equivalences in strong limit theorems for renewal counting processes," Statistics & Probability Letters, Elsevier, vol. 35(4), pages 381-394, November.
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    Cited by:

    1. Xuejun Wang & Zeyu Si, 2015. "Complete consistency of the estimator of nonparametric regression model under ND sequence," Statistical Papers, Springer, vol. 56(3), pages 585-596, August.
    2. Rosalsky, Andrew & Stoica, George, 2010. "On the strong law of large numbers for identically distributed random variables irrespective of their joint distributions," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1265-1270, September.
    3. Soo Sung, 2012. "Complete convergence for weighted sums of negatively dependent random variables," Statistical Papers, Springer, vol. 53(1), pages 73-82, February.

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