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Limiting behavior of weighted sums of i.i.d. random variables

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  • Pingyan, Chen
  • Shixin, Gan

Abstract

The strong laws of large numbers, Chover's laws of the iterated logarithm (LIL) and laws of the single logarithm are established for weighted sums of i.i.d. random variables under suitable conditions on both the weights and the distribution.

Suggested Citation

  • Pingyan, Chen & Shixin, Gan, 2007. "Limiting behavior of weighted sums of i.i.d. random variables," Statistics & Probability Letters, Elsevier, vol. 77(16), pages 1589-1599, October.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:16:p:1589-1599
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    References listed on IDEAS

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    1. Peng, Liang & Qi, Yongcheng, 2003. "Chover-type laws of the iterated logarithm for weighted sums," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 401-410, December.
    2. Pingyan, Chen, 2002. "Limiting behavior of weighted sums with stable distributions," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 367-375, December.
    3. Sung, Soo Hak, 2001. "Strong laws for weighted sums of i.i.d. random variables," Statistics & Probability Letters, Elsevier, vol. 52(4), pages 413-419, May.
    4. Bai, Z. D. & Cheng, Philip E., 2000. "Marcinkiewicz strong laws for linear statistics," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 105-112, January.
    5. Rosalsky, Andrew & Sreehari, M., 1998. "On the limiting behavior of randomly weighted partial sums," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 403-410, November.
    6. Wu, Wei Biao, 1999. "On the strong convergence of a weighted sum," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 19-22, August.
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    Cited by:

    1. Soo Sung, 2011. "On the strong convergence for weighted sums of random variables," Statistical Papers, Springer, vol. 52(2), pages 447-454, May.

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