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A remark on LSL for weighted sums of i.i.d random elements

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  • Chen, Pingyan
  • Chen, Ran

Abstract

In the paper, the upper bound and lower bound of the law of the single logarithm (LSL) are established under the condition that the sequence of the normalized weighted sums of random elements is bounded in probability. The main result improves the upper bound in [Sung, S.H., 2009. A law of the single logarithm for weighted sums of i.i.d. random elements. Statist. Probab. Lett., 79, 1351-1357] and hence extends the result in [Chen, P., Gan, S., 2007. Limiting behavior of weighted sums of i.i.d. random variables. Statist. Probab. Lett., 77, 1589-1599].

Suggested Citation

  • Chen, Pingyan & Chen, Ran, 2010. "A remark on LSL for weighted sums of i.i.d random elements," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1329-1334, September.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:17-18:p:1329-1334
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    References listed on IDEAS

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    1. 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.
    2. Li, D. L. & Rao, M. B. & Wang, X. C., 1995. "On the Strong Law of Large Numbers and the Law of the Logarithm for Weighted Sums of Independent Random Variables with Multidimensional Indices," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 181-198, February.
    3. Bai, Z. D. & Cheng, Philip E., 2000. "Marcinkiewicz strong laws for linear statistics," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 105-112, January.
    4. Wu, Wei Biao, 1999. "On the strong convergence of a weighted sum," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 19-22, August.
    5. Li, Deli & Huang, Mei Ling, 1998. "A note on moments of the maximum of Cesàro summation," Statistics & Probability Letters, Elsevier, vol. 38(1), pages 73-81, May.
    6. Li, Deli, 1996. "Bounded and compact laws of the logarithm for B-valued random variables," Stochastic Processes and their Applications, Elsevier, vol. 63(2), pages 189-209, November.
    7. Sung, Soo Hak, 2009. "A law of the single logarithm for weighted sums of i.i.d. random elements," Statistics & Probability Letters, Elsevier, vol. 79(10), pages 1351-1357, May.
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