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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

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.

Suggested Citation

  • Chen, Pingyan & Hao, Chunyan, 2011. "A remark on the law of the logarithm for weighted sums of random variables with multidimensional indices," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1808-1812.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:12:p:1808-1812
    DOI: 10.1016/j.spl.2011.07.007
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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    Keywords

    Law of the logarithm; Weighted sum;

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