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A remark on the law of the logarithm for weighted sums of random variables with multidimensional indices

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  • Chen, Pingyan
  • Hao, Chunyan
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    Abstract

    In this work, a sharp upper bound on the law of the logarithm for the weighted sums of random variables with multidimensional indices is obtained. The main result improves the result in [Li, Rao and Wang, 1995. On strong law of large numbers and the law of the logarithm for weighted sums of independent random variables with multidimensional indices. J. Multivariate Anal. 52, 181–198], partly.

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    Bibliographic Info

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

    Volume (Year): 81 (2011)
    Issue (Month): 12 ()
    Pages: 1808-1812

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    Handle: RePEc:eee:stapro:v:81:y:2011:i:12:p:1808-1812

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    Keywords: Law of the logarithm; Weighted sum;

    References

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    1. Kaffes, D. & Bhaskara Rao, M., 1982. "Weak consistency of least-squares estimators in linear models," Journal of Multivariate Analysis, Elsevier, vol. 12(2), pages 186-198, June.
    2. Gu, Wentao & Roussas, George G. & Tran, Lanh T., 2007. "On the convergence rate of fixed design regression estimators for negatively associated random variables," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1214-1224, July.
    3. 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.
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